SwePub - search: L773:0025 5718 OR L773:1088 68...

Enumeration	Reference	Cover	Find
1.	Målqvist, Axel, 1978, et al. (author) Localization of elliptic multiscale problems 2014 In: Mathematics of Computation. - 1088-6842 .- 0025-5718. ; 83:290, s. 2583-2603 Journal article (peer-reviewed)abstract This paper constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients. The basis functions are solutions of local problems on vertex patches. The error of the corresponding generalized finite element method decays exponentially with respect to the number of layers of elements in the patches. Hence, on a uniform mesh of size $ H$, patches of diameter $ H\log (1/H)$ are sufficient to preserve a linear rate of convergence in $ H$ without pre-asymptotic or resonance effects. The analysis does not rely on regularity of the solution or scale separation in the coefficient. This result motivates new and justifies old classes of variational multiscale methods. - See more at: http://www.ams.org/journals/mcom/2014-83-290/S0025-5718-2014-02868-8/#sthash.z2CCFXIg.dpuf
2.	Hakberg, Bengt, 1939 (author) A Discrete KPP-Theory for Fisher's Equation 2013 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 82:282, s. 781-802 Journal article (peer-reviewed)abstract The purpose of this paper is to extend the theory by Kolmogorov, Petrowsky and Piscunov (KPP) for Fisher's equation, to a discrete solution. We approximate the time derivative in Fisher's equation by an explicit Euler scheme and the diffusion operator by a symmetric difference scheme of second order. We prove that the discrete solution converges towards a traveling wave, under restrictions in the time-and space-widths, as the number of time steps increases to infinity. We also prove that the flame velocity can be determined as a solution to an optimization problem.
3.	Sheen, D, et al. (author) A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature 2000 In: Math. Comp.. - 0025-5718 .- 1088-6842. ; 69:229, s. 177-195 Journal article (peer-reviewed)abstract We treat the time discretization of an initial-value problem for a homogeneous abstract parabolic equation by first using a representation of the solution as an integral along the boundary of a sector in the right half of the complex plane, then transforming this into a real integral on the finite interval , and finally applying a standard quadrature formula to this integral. The method requires the solution of a finite set of elliptic problems with complex coefficients, which are independent and may therefore be done in parallel. The method is combined with spatial discretization by finite elements.
4.	Asadzadeh, Mohammad, 1952, et al. (author) A new approach to Richardson extrapolation in the finite element method for second order elliptic problems 2009 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 78:4, s. 1951-1973 Journal article (peer-reviewed)abstract This paper presents a nonstandard local approach to Richardson extrapolation, when it is used to increase the accuracy of the standard finite element approximation of solutions of second order elliptic boundary value problems in $ \mathbb{R}^N$, $ N \ge 2$. The main feature of the approach is that it does not rely on a traditional asymptotic error expansion, but rather depends on a more easily proved weaker a priori estimate, derived in [19], called an asymptotic error expansion inequality. In order to use this inequality to verify that the Richardson procedure works at a point, we require a local condition which links the different subspaces used for extrapolation. Roughly speaking, this condition says that the subspaces are similar about a point, i.e., any one of them can be made to locally coincide with another by a simple scaling of the independent variable about that point. Examples of finite element subspaces that occur in practice and satisfy this condition are given.
5.	Avelin, Helen (author) Computations of Eisenstein series on Fuchsian groups 2008 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 77:263, s. 1779-1800 Journal article (peer-reviewed)abstract We present numerical investigations of the value distribution and distribution of Fourier coefficients of the Eisenstein series E(z, s) on arithmetic and non-arithmetic Fuchsian groups. Our numerics indicate a Gaussian limit value distribution for a real- valued rotation of E(z; s) as Res = 1/2, Im s -> , infinity and also, on non-arithmetic groups, a complex Gaussian limit distribution for E(z, s) when Res > , 1/2 near 1/2 and Im s -> , infinity at least if we allow Re s. 1/2 at some rate. Furthermore, on non-arithmetic groups and for fixed s with Re s = 1/2 near 1/2, our numerics indicate a Gaussian limit distribution for the appropriately normalized Fourier coefficients.
6.	Avelin, Helen (author) Deformation of Γ0(5)-cusp forms 2007 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 76:257, s. 361-384 Journal article (peer-reviewed)abstract We develop an algorithm for numerical computation of the Eisenstein series on a Riemann surface of constant negative curvature. We focus in particular on the computation of the poles of the Eisenstein series. Using our numerical methods, we study the spectrum of the Laplace-Beltrami operator as the surface is being deformed. Numerical evidence of the destruction of $ \Gamma_0(5)$-cusp forms is presented.
7.	Axelsson, Owe, et al. (author) The local Green's function method in singularly perturbed convection-diffusion problems 2009 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 78:265, s. 153-170 Journal article (peer-reviewed)
8.	Björn, Anders, et al. (author) Factors of generalized fermat numbers 1998 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 67:221, s. 441-446 Journal article (peer-reviewed)
9.	Björn, Anders, et al. (author) FACTORS OF GENERALIZED FERMAT NUMBERS (vol 67, pg 441, 1998) : Table errata 2 2011 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 80:275, s. 1865-1866 Journal article (peer-reviewed)abstract We note that one more factor is missing from Table 1 in Bjorn-Riesel, Factors of generalized Fermat numbers, Math. Comp. 67 (1998), 441 446, in addition to the three already reported upon in Bjorn-Riesel, Table errata to "Factors of generalized Fermat numbers", Math. Comp. 74 (2005), p. 2099.
10.	Björn, Anders, et al. (author) Factors of generalized fermat numbers (vol 67, pg 441, 1998) 2005 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 74:252, s. 2099-2099 Journal article (peer-reviewed)abstract We note that three factors are missing from Table 1 in Factors of generalized Fermat numbers by A. Bjorn and H. Riesel published in Math. Comp. 67 (1998), 441-446.
11.	Chatzipantelidis, P., et al. (author) Some error estimates for the lumped mass finite element method for a parabolic problem 2012 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 81:277, s. 1-20 Journal article (peer-reviewed)abstract We study the spatially semidiscrete lumped mass method for the model homogeneous heat equation with homogeneous Dirichlet boundary conditions. Improving earlier results we show that known optimal order smooth initial data error estimates for the standard Galerkin method carry over to the lumped mass method whereas nonsmooth initial data estimates require special assumptions on the triangulation. We also discuss the application to time discretization by the backward Euler and Crank-Nicolson methods.
12.	Demlow, Alan, et al. (author) Local pointwise a posteriori gradient error bounds for the Stokes equations 2013 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 82:282, s. 625-649 Journal article (peer-reviewed)abstract We consider the standard Taylor-Hood finite element method for the stationary Stokes system on polyhedral domains. We prove local a posteriori error estimates for the maximum error in the gradient of the velocity field. Because the gradient of the velocity field blows up near reentrant corners and edges, such local error control is necessary when pointwise control of the gradient error is desirable. Computational examples confirm the utility of our estimates in adaptive codes.
13.	Elliott, Charles M., et al. (author) Error estimates with smooth and nonsmooth data for a finite element method for the Cahn-Hilliard equation 1992 In: Math. Comp.. - 0025-5718 .- 1088-6842. ; 58:198 Journal article (peer-reviewed)abstract A finite element method for the Cahn-Hilliard equation (a semilinear parabolic equation of fourth order) is analyzed, both in a spatially semidiscrete case and in a completely discrete case based on the backward Euler method. Error bounds of optimal order over a finite time interval are obtained for solutions with smooth and nonsmooth initial data. A detailed study of the regularity of the exact solution is included. The analysis is based on local Lipschitz conditions for the nonlinearity with respect to Sobolev norms, and the existence of a Ljapunov functional for the exact and the discretized equations is essential. A result concerning the convergence of the attractor of the corresponding approximate nonlinear semigroup (upper semicontinuity with respect to the discretization parameters) is obtained as a simple application of the nonsmooth data error estimate.
14.	Engquist, Björn, et al. (author) Heterogeneous multiscale methods for stiff ordinary differential equations 2005 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 74:252, s. 1707-1742 Journal article (peer-reviewed)abstract The heterogeneous multiscale methods (HMM) is a general framework for the numerical approximation of multiscale problems. It is here developed for ordinary differential equations containing different time scales. Stability and convergence results for the proposed HMM methods are presented together with numerical tests. The analysis covers some existing methods and the new algorithms that are based on higher-order estimates of the effective force by kernels satisfying certain moment conditions and regularity properties. These new methods have superior computational complexity compared to traditional methods for stiff problems with oscillatory solutions.
15.	Eriksson, Jerry, et al. (author) Local results for the Gauss-Newton method on constrained rank-deficient nonlinear least squares 2004 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 73:248, s. 1865-1883 Journal article (peer-reviewed)abstract A nonlinear least squares problem with nonlinear constraints may be ill posed or even rank-deficient in two ways. Considering the problem formulated as $min_{x} 1/2Vert f_{2}(x) Vert _{2}^{2}$subject to the constraints $f_{1}(x) = 0$, the Jacobian $J_{1} = partial f_{1}/ partial x$ and/or the Jacobian $J = partial f/ partial x$, $f = [f_{1};f_{2}]$, may be ill conditioned at the solution. We analyze the important special case when $J_{1}$ and/or $J$ do not have full rank at the solution. In order to solve such a problem, we formulate a nonlinear least norm problem. Next we describe a truncated Gauss-Newton method. We show that the local convergence rate is determined by the maximum of three independent Rayleigh quotients related to three different spaces in $mathbb{R} ^{n}$. Another way of solving an ill-posed nonlinear least squares problem is to regularize the problem with some parameter that is reduced as the iterates converge to the minimum. Our approach is a Tikhonov based local linear regularization that converges to a minimum norm problem. This approach may be used both for almost and rank-deficient Jacobians. Finally we present computational tests on constructed problems verifying the local analysis.
16.	Gallouët, Thierry, et al. (author) Convergence of a finite volume scheme for the convection-diffusion equation with L1 data 2012 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 81:279, s. 1429-1454 Journal article (peer-reviewed)abstract In this paper, we prove the convergence of a finite-volume schemefor the time-dependent convection–diffusion equation with an L1 right-handside. To this purpose, we first prove estimates for the discrete solution andfor its discrete time and space derivatives. Then we show the convergence of asequence of discrete solutions obtained with more and more refined discretiza-tions, possibly up to the extraction of a subsequence, to a function which metsthe regularity requirements of the weak formulation of the problem; to thispurpose, we prove a compactness result, which may be seen as a discrete ana-logue to Aubin-Simon’s lemma. Finally, such a limit is shown to be indeed aweak solution.
17.	Granger, Robert, et al. (author) Generalised mersenne numbers revisited 2013 In: Mathematics of Computation. - : American Mathematical Society. - 0025-5718 .- 1088-6842. ; 82:284, s. 2389-2420 Journal article (peer-reviewed)abstract Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus making them an attractive choice for modular multiplication implementation. However, the issue of residue multiplication efficiency seems to have been overlooked. Asymptotically, using a cyclic rather than a linear convolution, residue multiplication modulo a Mersenne number is twice as fast as integer multiplication; this property does not hold for prime GMNs, unless they are of Mersenne's form. In this work we exploit an alternative generalisation of Mersenne numbers for which an analogue of the above property - and hence the same efficiency ratio - holds, even at bitlengths for which schoolbook multiplication is optimal, while also maintaining very efficient reduction. Moreover, our proposed primes are abundant at any bitlength, whereas GMNs are extremely rare. Our multiplication and reduction algorithms can also be easily parallelised, making our arithmetic particularly suitable for hardware implementation. Furthermore, the field representation we propose also naturally protects against side-channel attacks, including timing attacks, simple power analysis and differential power analysis, which is essential in many cryptographic scenarios, in constrast to GMNs.
18.	Liu, Hailiang, et al. (author) Error estimates for Gaussian beam superpositions 2013 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 82:282, s. 919-952 Journal article (peer-reviewed)abstract Gaussian beams are asymptotically valid high frequency solutions to hyperbolic partial differential equations, concentrated on a single curve through the physical domain. They can also be extended to some dispersive wave equations, such as the Schrodinger equation. Superpositions of Gaussian beams provide a powerful tool to generate more general high frequency solutions that are not necessarily concentrated on a single curve. This work is concerned with the accuracy of Gaussian beam superpositions in terms of the wavelength epsilon. We present a systematic construction of Gaussian beam superpositions for all strictly hyperbolic and Schrodinger equations subject to highly oscillatory initial data of the form Ae(i Phi/) (epsilon). Through a careful estimate of an oscillatory integral operator, we prove that the k-th order Gaussian beam superposition converges to the original wave field at a rate proportional to epsilon(k/2) in the appropriate norm dictated by the well-posedness estimate. In particular, we prove that the Gaussian beam superposition converges at this rate for the acoustic wave equation in the standard, epsilon-scaled, energy norm and for the Schrodinger equation in the L-2 norm. The obtained results are valid for any number of spatial dimensions and are unaffected by the presence of caustics. We present a numerical study of convergence for the constant coefficient acoustic wave equation in R-2 to analyze the sharpness of the theoretical results.
19.	Möller, Niels (author) On Schonhage's algorithm and subquadratic integer GCD computation 2008 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 77:261, s. 589-607 Journal article (peer-reviewed)abstract We describe a new subquadratic left-to-right GCD algorithm, inspired by Schonhage's algorithm for reduction of binary quadratic forms, and compare it to the first subquadratic GCD algorithm discovered by Knuth and Schonhage, and to the binary recursive GCD algorithm of Stehle and Zimmer-mann. The new GCD algorithm runs slightly faster than earlier algorithms, and it is much simpler to implement. The key idea is to use a stop condition for HGCD that is based not on the size of the remainders, but on the size of the next difference. This subtle change is sufficient to eliminate the back-up steps that are necessary in all previous subquadratic left-to-right GCD algorithms. The subquadratic GCD algorithms all have the same asymptotic running time, O(n(log n)(2) log log n).
20.	Sjögreen, Björn, et al. (author) A model for peak formation in the two-phase equations 2007 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 76:260, s. 1925-1940 Journal article (peer-reviewed)abstract We present a hyperbolic-elliptic model problem related to the equations of two-phase fluid flow. The model problem is solved numerically, and properties of its solution are presented. The model equation is well-posed when linearized around a constant state, but there is a strong focusing effect, and very large solutions exist at certain times. We prove that the model problem has a smooth solution for bounded times.
21.	Thomee, Vidar, 1933, et al. (author) On the existence of maximum principles in parabolic finite element equations 2008 In: Math. Comp.. - 0025-5718 .- 1088-6842. ; 77:261, s. 11-19 Journal article (peer-reviewed)abstract In 1973, H. Fujii investigated discrete versions of the maximum principle for the model heat equation using piecewise linear finite elements in space. In particular, he showed that the lumped mass method allows a maximum principle when the simplices of the triangulation are acute, and this is known to generalize in two space dimensions to triangulations of Delauney type. In this note we consider more general parabolic equations and first show that a maximum principle cannot hold for the standard spatially semidiscrete problem. We then show that for the lumped mass method the above conditions on the triangulation are essentially sharp. This is in contrast to the elliptic case in which the requirements are weaker. We also study conditions for the solution operator acting on the discrete initial data, with homogeneous lateral boundary conditions, to be a contraction or a positive operator.
22.	Verdier, Olivier (author) Reductions of Operator Pencils 2014 In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 83:285, s. 189-214 Journal article (peer-reviewed)abstract We study problems associated with an operator pencil, i.e., a pair of operators onBanach spaces. Two natural problems to consider are linear constrained dierentialequations and the description of the generalized spectrum. The main tool to tackleeither of those problems is the reduction of the pencil. There are two kinds of naturalreduction operations associated to a pencil, which are conjugate to each other.Our main result is that those two kinds of reductions commute, under some mildassumptions that we investigate thoroughly.Each reduction exhibits moreover a pivot operator. The invertibility of all thepivot operators of all possible successive reductions corresponds to the notion ofregular pencil in the nite dimensional case, and to the inf-sup condition for saddlepoint problems on Hilbert spaces.Finally, we show how to use the reduction and the pivot operators to describe thegeneralized spectrum of the pencil.
23.	Engquist, Björn, et al. (author) Nonlinear filters for efficient shock computation 1989 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 52:186, s. 509-537 Journal article (peer-reviewed)abstract A new type of methods for the numerical approximation of hyperbolic conservation laws with discontinuous solution is introduced. The methods are based on standard finite difference schemes. The difference solution is processed with a nonlinear conservation form filter at every time level to eliminate spurious oscillations near shocks. It is proved that the filter can control the total variation of the solution and also produce sharp discrete shocks. The method is simpler and faster than many other high resolution schemes for shock calculations. Numerical examples in one and two space dimensions are presented.
24.	Engquist, Björn, et al. (author) Stable and entropy satisfying approximations for transonic flow calculations 1980 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 34:149, s. 45-75 Journal article (peer-reviewed)abstract Finite difference approximations for the small disturbance equation of transonic flow are developed and analyzed. New schemes of the Cole-Murman type are presented fpr which nonlinear stability is proved. The Cole-Murman scheme may have entropy violating expansion shocks as solutions. In the new schemes the switch between the subsonic and supersonic domains is designed such that these nonphysical shocks are guaranteed not to occur. Results from numercial calculations are given which illustrate these conclusions
25.	Engquist, Björn, et al. (author) Steady state computations for wave propagation problems 1987 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 49, s. 39-64 Journal article (peer-reviewed)abstract The behavior of difference approximations of hyperbolic partial differential equations as time t → ∞ is studied. The rate of convergence to steady state is analyzed theoretically and expe imentally for the advection equation and the linearized Euler equations. The choice of difference formulas and boundary conditions strongly influences the rate of convergence in practical steady state calculations. In particular it is shown that upwind difference methods and characteristic boundary conditions have very attractive convergence properties
26.	Johnson, Claes, et al. (author) On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws 1990 In: Mathematics of Computation. - PROVIDENCE : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 54:189, s. 107-129 Journal article (peer-reviewed)abstract We extend our previous analysis of streamline diffusion finite element methods for hyperbolic systems of conservation laws to include a shock-capturing term adding artificial viscosity depending on the local absolute value of the residual of the finite element solution and the meh size. With this term present, we prove a maximum norm bound for finite element solutionsof Burgers' equation an thus complete an earlier convergence proof for this equation. We further prove, using entropy variables, that a strong limit of finite element solutions is a weak solution of the system of conservation laws and satisfies the entropy inequality asociated with the entropy variables. Results of some numerical experiments for the time-dependent compressible Euler equations in two dimensions are also reported.
27.	Kublik, Catherine, et al. (author) An extrapolative approach to integration over hypersurfaces in the level set framework 2018 In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 87:313, s. 2365-2392 Journal article (peer-reviewed)abstract We provide a new approach for computing integrals over hypersurfaces in the level set framework. The method is based on the discretization (via simple Riemann sums) of the classical formulation used in the level set framework, with the choice of specific kernels supported on a tubular neighborhood around the interface to approximate the Dirac delta function. The novelty lies in the choice of kernels, specifically its number of vanishing moments, which enables accurate computations of integrals over a class of closed, continuous, piecewise smooth, curves or surfaces; e.g., curves in two dimensions that contain a finite number of corners. We prove that for smooth interfaces, if the kernel has enough vanishing moments (related to the dimension of the embedding space), the analytical integral formulation coincides exactly with the integral one wishes to calculate. For curves with corners and cusps, the formulation is not exact but we provide an analytical result relating the severity of the corner or cusp with the width of the tubular neighborhood. We show numerical examples demonstrating the capability of the approach, especially for integrating over piecewise smooth interfaces and for computing integrals where the integrand is only Lipschitz continuous or has an integrable singularity.
28.	Starius, Göran (author) Asymptotic expansions for a class of elliptic difference schemes 1981 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 37:156, s. 321-326 Journal article (peer-reviewed)abstract This paper derives an asymptotic expansion of the global error for Kreiss' difference scheme for the Dirichlet problem for Poisson's equation. This scheme, combined with a deferred correction procedure or the Richardson extrapolation technique, yields a method of accuracy at least O(h6.5) in L2, where h is the mesh length.
29.	Szepessy, Anders, 1960-, et al. (author) On the convergence of a finite element method for a nonlinear hyperbolic conservation law 1987 In: Mathematics of Computation. - PROVIDENCE : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 49:180, s. 427-444 Journal article (peer-reviewed)
30.	Westerholt-Raum, Martin, 1985 (author) Computing genus 1 Jacobi forms 2016 In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 85:298, s. 931-960 Journal article (peer-reviewed)abstract We develop an algorithm to compute Fourier expansions of vector valued modular forms for Weil representations. As an application, we compute explicit linear equivalences of special divisors on modular varieties of orthogonal type. We define three families of Hecke operators for Jacobi forms, and analyze the induced action on vector valued modular forms. The newspaces attached to one of these families are used to give a more memory efficient version of our algorithm. - See more at: http://www.ams.org/journals/mcom/2016-85-298/S0025-5718-2015-02992-5/#sthash.bv7cxz8N.dpuf
31.	Abdulle, Assyr, et al. (author) Localized orthogonal decomposition method for the wave equation with a continuum of scales 2017 In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 86:304, s. 549-587 Journal article (peer-reviewed)abstract This paper is devoted to numerical approximations for the wave equation with a multiscale character. Our approach is formulated in the framework of the Localized Orthogonal Decomposition (LOD) interpreted as a numerical homogenization with an L2-projection. We derive explicit convergence rates of the method in the L∞(L2)-, W1,∞(L2)-and L∞(H1)-norms without any assumptions on higher order space regularity or scale-separation. The order of the convergence rates depends on further graded assumptions on the initial data. We also prove the convergence of the method in the framework of G-convergence without any structural assumptions on the initial data, i.e. without assuming that it is well-prepared. This rigorously justifies the method. Finally, the performance of the method is demonstrated in numerical experiments.
32.	Altmann, R., et al. (author) Semi-explicit discretization schemes for weakly coupled elliptic-parabolic problems 2021 In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 90:329, s. 1089-1118 Journal article (peer-reviewed)abstract We prove first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for elliptic-parabolic problems which are weakly coupled. This setting includes poroelasticity, thermoelasticity, as well as multiple-network models used in medical applications. The semi-explicit approach decouples the system such that each time step requires the solution of two small and well-structured linear systems rather than the solution of one large system. The decoupling improves the computational efficiency without decreasing the convergence rates. The presented convergence proof is based on an interpretation of the scheme as an implicit method applied to a constrained partial differential equation with delay term. Here, the delay time equals the used step size. This connection also allows a deeper understanding of the weak coupling condition, which we accomplish to quantify explicitly.
33.	Andersson, Adam, 1979, et al. (author) Weak convergence for a spatial approximation of the nonlinear stochastic heat equation 2016 In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 85, s. 1335-1358 Journal article (peer-reviewed)abstract We find the weak rate of convergence of the spatially semidiscrete finite element approximation of the nonlinear stochastic heat equation. Both multiplicative and additive noise is considered under different assumptions. This extends an earlier result of Debussche in which time discretization is considered for the stochastic heat equation perturbed by white noise. It is known that this equation has a solution only in one space dimension. In order to obtain results for higher dimensions, colored noise is considered here, besides white noise in one dimension. Integration by parts in the Malliavin sense is used in the proof. The rate of weak convergence is, as expected, essentially twice the rate of strong convergence.
34.	Apelkrans, Mats Y. T. (author) On difference schemes for hyperbolic equations with discontinuous initial values 1968 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 22:103, s. 525-539 Journal article (peer-reviewed)
35.	Ariel, Gil, et al. (author) A multiscale method for stiff ordinary differential equations with resonance 2009 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 78:266, s. 929-956 Journal article (peer-reviewed)abstract A multiscale method for computing the effective behavior of a class of stiff and highly oscillatory ordinary differential equations (ODEs) is presented. The oscillations may be in resonance with one another and thereby generate hidden slow dynamics. The proposed method relies on correctly tracking a set of slow variables whose dynamics is closed up to perturbation, and is sufficient to approximate any variable and functional that are slow under the dynamics of the ODE. This set of variables is detected numerically as a preprocessing step in the numerical methods. Error and complexity estimates are obtained. The advantages of the method is demonstrated with a few examples, including a commonly studied problem of Fermi, Pasta, and Ulam.
36.	Bilarev, Todor, et al. (author) On the speed of convergence of Newton's method for complex polynomials 2016 In: Mathematics of Computation. - : American Mathematical Society (AMS). - 1088-6842 .- 0025-5718. ; 85:298, s. 693-705 Journal article (peer-reviewed)abstract We investigate Newton's method for complex polynomials of arbitrary degree d, normalized so that all their roots are in the unit disk. For each degree d, we give an explicit set S-d of 3.33d log(2) d(1 + o(1)) points with the following universal property: for every normalized polynomial of degree d there are d starting points in S-d whose Newton iterations find all the roots with a low number of iterations: if the roots are uniformly and independently distributed, we show that with probability at least 1-2/d the number of iterations for these d starting points to reach all roots with precision epsilon is O(d(2) log(4) d + d log vertical bar log epsilon vertical bar). This is an improvement of an earlier result by Schleicher, where the number of iterations is shown to be O(d(4) log(2) d + d(3) log(2) d vertical bar log epsilon vertical bar) in the worst case (allowing multiple roots) and O(d(3) log(2) d(log d + log delta) + d log vertical bar log epsilon vertical bar) for well-separated (so-called delta-separated) roots. Our result is almost optimal for this kind of starting points in the sense that the number of iterations can never be smaller than O(d(2)) for fixed e. It provides theoretical support for an empirical study, by Schleicher and Stoll, in which all roots of polynomials of degree 10(6) and more were found efficiently.
37.	Björn, Anders, et al. (author) Correction: FACTORS OF GENERALIZED FERMAT NUMBERS (vol 67, No. 221, pg 441-446, 1998) 2011 In: Mathematics of Computation. - : American Mathematical Society. - 0025-5718 .- 1088-6842. ; 80:275, s. 1865-1866 Journal article (peer-reviewed)abstract We note that one more factor is missing from Table 1 in Bjorn-Riesel, Factors of generalized Fermat numbers, Math. Comp. 67 (1998), 441 446, in addition to the three already reported upon in Bjorn-Riesel, Table errata to "Factors of generalized Fermat numbers", Math. Comp. 74 (2005), p. 2099.
38.	Bolin, David, et al. (author) REGULARITY AND NUMERICAL APPROXIMATION OF FRACTIONAL ELLIPTIC DIFFERENTIAL EQUATIONS ON COMPACT METRIC GRAPHS 2024 In: Mathematics of Computation. - 1088-6842 .- 0025-5718. ; 93:349, s. 2439-2472 Journal article (peer-reviewed)abstract The fractional differential equation L(beta)u = f posed on a compact metric graph is considered, where beta > 0 and L = kappa(2) - del(a del ) is a second order elliptic operator equipped with certain vertex conditions and sufficiently smooth and positive coefficients kappa, a. We demonstrate the existence of a unique solution for a general class of vertex conditions and derive the regularity of the solution in the specific case of Kirchhoff vertex conditions. These results are extended to the stochastic setting when f is replaced by Gaussian white noise. For the deterministic and stochastic settings under generalized Kirchhoff vertex conditions, we propose a numerical solution based on a finite element approximation combined with a rational approximation of the fractional power L-beta. For the resulting approximation, the strong error is analyzed in the deterministic case, and the strong mean squared error as well as the L-2( Gamma x Gamma )error of the covariance function of the solution are analyzed in the stochastic setting. Explicit rates of convergences are derived for all cases. Numerical experiments for L = kappa(2) - del, kappa > 0 are performed to illustrate the results.
39.	Brehier, C. E., et al. (author) Splitting integrators for stochastic Lie–Poisson systems 2023 In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 92, s. 2167-2216 Journal article (peer-reviewed)abstract . We study stochastic Poisson integrators for a class of stochastic Poisson systems driven by Stratonovich noise. Such geometric integrators preserve Casimir functions and the Poisson map property. For this purpose, we propose explicit stochastic Poisson integrators based on a splitting strategy, and analyse their qualitative and quantitative properties: preservation of Casimir functions, existence of almost sure or moment bounds, asymptotic preserving property, and strong and weak rates of convergence. The construction of the schemes and the theoretical results are illustrated through extensive numerical experiments for three examples of stochastic Lie-Poisson systems, namely: stochastically perturbed Maxwell-Bloch, rigid body and sine-Euler equations.
40.	Brenan, K.E., et al. (author) Backward differentiation approximations of nonlinear differential/algebraic systems 1988 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 51:84, s. 659-676 Journal article (peer-reviewed)abstract Finite-difference approximations of dynamical systems modeled by nonlinear, semiexplicit, differential/algebraic equations are analyzed. Convergence for the backward differentiation method is proved for index two and index three problems when the numerical initial values obey certain constraints. The appropriate asymptotic convergence rates and the leading error terms are determined.
41.	Browning, Gerald, et al. (author) Mesh refinement 1973 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 27:121, s. 29-39 Journal article (peer-reviewed)
42.	Burman, Erik, et al. (author) A cut finite element method with boundary value correction 2018 In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 87:310, s. 633-657 Journal article (peer-reviewed)abstract In this contribution we develop a cut finite element method with boundary value correction of the type originally proposed by Bramble, Dupont, and Thomee in [Math. Comp. 26 (1972), 869-879]. The cut finite element method is a fictitious domain method with Nitsche-type enforcement of Dirich-let conditions together with stabilization of the elements at the boundary which is stable and enjoy optimal order approximation properties. A computational difficulty is, however, the geometric computations related to quadrature on the cut elements which must be accurate enough to achieve higher order approximation. With boundary value correction we may use only a piecewise linear approximation of the boundary, which is very convenient in a cut finite element method, and still obtain optimal order convergence. The boundary value correction is a modified Nitsche formulation involving a Taylor expansion in the normal direction compensating for the approximation of the boundary. Key to the analysis is a consistent stabilization term which enables us to prove stability of the method and a priori error estimates with explicit dependence on the meshsize and distance between the exact and approximate boundary.
43.	Burman, Erik, et al. (author) Low regularity estimates for CutFEM approximations of an elliptic problem with mixed boundary conditions 2024 In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 93:345, s. 35-54 Journal article (peer-reviewed)abstract We show error estimates for a cut finite element approximation of a second order elliptic problem with mixed boundary conditions. The error estimates are of low regularity type where we consider the case when the exact solution u ∈ Hs with s ∈ (1, 3/2]. For Nitsche type methods this case requires special handling of the terms involving the normal flux of the exact solution at the the boundary. For Dirichlet boundary conditions the estimates are optimal, whereas in the case of mixed Dirichlet-Neumann boundary conditions they are suboptimal by a logarithmic factor.
44.	Burman, Erik, et al. (author) Stabilized nonconforming finite element methods for data assimilation in incompressible flows 2018 In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 87:311, s. 1029-1050 Journal article (peer-reviewed)abstract We consider a stabilized nonconforming finite element method for data assimilation in incompressible flow subject to the Stokes equations. The method uses a primal dual structure that allows for the inclusion of nonstandard data. Error estimates are obtained that are optimal compared to the conditional stability of the ill-posed data assimilation problem.
45.	Courcy-Ireland, Matthew de, 1989-, et al. (author) Six-dimensional sphere packing and linear programming 2024 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. Journal article (peer-reviewed)abstract We prove that the Cohn-Elkies linear programming bound for sphere packing is not sharp in dimension 6. The proof uses duality and optimization over a space of modular forms, generalizing a construction of Cohn- Triantafillou [Math. Comp. 91 (2021), pp. 491-508] to the case of odd weight and non-trivial character.
46.	Courcy-Ireland, Matthew de, 1989-, et al. (author) Six-dimensional sphere packing and linear programming 2024 In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 93:348, s. 1993-2029 Journal article (peer-reviewed)abstract We prove that the Cohn–Elkies linear programming bound for sphere packing is not sharp in dimension 6. The proof uses duality and optimization over a space of modular forms, generalizing a construction of Cohn–Triantafillou [Math. Comp. 91 (2021), pp. 491–508] to the case of odd weight and non-trivial character.
47.	Di Rocco, Sandra, et al. (author) Sampling and Homology via Bottlenecks 2022 In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 91:338, s. 2969-2995 Journal article (peer-reviewed)abstract In this paper we present an efficient algorithm to produce a provably dense sample of a smooth compact affine variety. The procedure is partly based on computing bottlenecks of the variety. Using geometric information such as the bottlenecks and the local reach we also provide bounds on the density of the sample needed in order to guarantee that the homology of the variety can be recovered from the sample. An implementation of the algorithm is provided together with numerical experiments and a computational comparison to the algorithm by Dufresne et al. [Sampling real algebraic varieties for topological data analysis, arXiv:1802.07716, 2018].
48.	Donatelli, Marco, et al. (author) Spectral analysis and spectral symbol of matrices in isogeometric collocation methods 2016 In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 85:300, s. 1639-1680 Journal article (peer-reviewed)
49.	Dostert, Maria, et al. (author) Kissing number in non-euclidean spaces of constant sectional curvature 2021 In: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 90:331, s. 2507-2525 Journal article (peer-reviewed)abstract This paper provides upper and lower bounds on the kissing number of congruent radius r > 0 spheres in hyperbolic H-n and spherical S-n spaces, for n >= 2. For that purpose, the kissing number is replaced by the kissing function kappa(H)(n, r), resp. kappa(S)(n, r), which depends on the dimension n and the radius r. After we obtain some theoretical upper and lower bounds for kappa(H)(n, r), we study their asymptotic behaviour and show, in particular, that kappa(H)(n, r) similar to (n - 1) . d(n-1) . B(n-1/2, 1/2) . e((n-1)r), where d(n) is the sphere packing density in Rn, and B is the beta-function. Then we produce numeric upper bounds by solving a suitable semidefinite program, as well as lower bounds coming from concrete spherical codes. A similar approach allows us to locate the values of kappa(S)(n, r), for n = 3, 4, over subintervals in [0, pi] with relatively high accuracy.
50.	Engquist, Björn, et al. (author) Absorbing boundary conditions for the numerical simulation of waves 1997 In: Mathematics of Computation. - 0025-5718 .- 1088-6842. ; 1, s. 629-651 Journal article (peer-reviewed)abstract In practical calculations, it is often essential to introduce artificial boundaries to limit the area of computation. Here we develop a systematic method for obtaining a hierarchy of local boundary conditions at these artifical boundaries. These boundary conditions not only guarantee stable difference approximations, but also minimize the (unphysical) artificial reflections that occur at the boundaries.

Skapa referenser, mejla, bekava och länka

Permalink

Träfflista för sökning "L773:0025 5718 OR L773:1088 6842 "

Refine your search

Year