| 1. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
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A posteriori error estimates for streamline-diffusion and discontinuous Galerkin methods for the Vlasov-Maxwell system
- 2018
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Ingår i: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 58:1, s. 5-26
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Tidskriftsartikel (refereegranskat)abstract
- This paper concerns a posteriori error analysis for the streamline diffusion (SD) finite element method for the one and one-half dimensional relativistic Vlasov– Maxwell system. The SD scheme yields a weak formulation, that corresponds to an add of extra diffusion to, e.g. the system of equations having hyperbolic nature, or convection-dominated convection diffusion problems. The a posteriori error estimates rely on dual formulations and yield error controls based on the computable residuals. The convergence estimates are derived in negative norms, where the error is split into an iteration and an approximation error and the iteration procedure is assumed to converge.
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| 2. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
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A posteriori error estimates for the one and one-half Dimensional Relativistic Vlasov–Maxwell system
- 2018
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Ingår i: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 58:1, s. 5-26
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Tidskriftsartikel (refereegranskat)abstract
- © 2017 The Author(s) This paper concerns a posteriori error analysis for the streamline diffusion (SD) finite element method for the one and one-half dimensional relativistic Vlasov–Maxwell system. The SD scheme yields a weak formulation, that corresponds to an add of extra diffusion to, e.g. the system of equations having hyperbolic nature, or convection-dominated convection diffusion problems. The a posteriori error estimates rely on dual formulations and yield error controls based on the computable residuals. The convergence estimates are derived in negative norms, where the error is split into an iteration and an approximation error and the iteration procedure is assumed to converge.
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| 3. |
- Barth, A., et al.
(författare)
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Multilevel Monte Carlo method for parabolic stochastic partial differential equations
- 2013
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Ingår i: BIT (Copenhagen). - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 53:1, s. 3-27
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Tidskriftsartikel (refereegranskat)abstract
- We analyze the convergence and complexity of multilevel Monte Carlo discretizations of a class of abstract stochastic, parabolic equations driven by square integrable martingales. We show under low regularity assumptions on the solution that the judicious combination of low order Galerkin discretizations in space and an Euler-Maruyama discretization in time yields mean square convergence of order one in space and of order 1/2 in time to the expected value of the mild solution. The complexity of the multilevel estimator is shown to scale log-linearly with respect to the corresponding work to generate a single path of the solution on the finest mesh, resp. of the corresponding deterministic parabolic problem on the finest mesh. © 2012 Springer Science + Business Media B.V.
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| 4. |
- Bergström, Per, et al.
(författare)
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Efficient computation of the Gauss-Newton direction when fitting NURBS using ODR
- 2012
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Ingår i: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 52:3, s. 571-588
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Tidskriftsartikel (refereegranskat)abstract
- We consider a subproblem in parameter estimation using the Gauss-Newton algorithm with regularization for NURBS curve fitting. The NURBS curve is fitted to a set of data points in least-squares sense, where the sum of squared orthogonal distances is minimized. Control-points and weights are estimated. The knot-vector and the degree of the NURBS curve are kept constant. In the Gauss-Newton algorithm, a search direction is obtained from a linear overdetermined system with a Jacobian and a residual vector. Because of the properties of our problem, the Jacobian has a particular sparse structure which is suitable for performing a splitting of variables. We are handling the computational problems and report the obtained accuracy using different methods, and the elapsed real computational time. The splitting of variables is a two times faster method than using plain normal equations.
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| 5. |
- Björck, Åke, et al.
(författare)
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Axel Ruhe 1942-2015
- 2015
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Ingår i: BIT Numerical Mathematics. - : Springer. - 0006-3835 .- 1572-9125. ; 55:3, s. 621-623
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Axel Ruhe passed away April 4, 2015. He was cross-country-skiing with friends in the Swedish mountains when after 21 km he suddenly died. He is survived by his wife Gunlaug and three children from his first marriage....
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| 6. |
- Björk, T., et al.
(författare)
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Monte Carlo Euler approximations of HJM term structure financial models
- 2013
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Ingår i: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 53:2, s. 341-383
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Tidskriftsartikel (refereegranskat)abstract
- We present Monte Carlo-Euler methods for a weak approximation problem related to the Heath-Jarrow-Morton (HJM) term structure model, based on Itô stochastic differential equations in infinite dimensional spaces, and prove strong and weak error convergence estimates. The weak error estimates are based on stochastic flows and discrete dual backward problems, and they can be used to identify different error contributions arising from time and maturity discretization as well as the classical statistical error due to finite sampling. Explicit formulas for efficient computation of sharp error approximation are included. Due to the structure of the HJM models considered here, the computational effort devoted to the error estimates is low compared to the work to compute Monte Carlo solutions to the HJM model. Numerical examples with known exact solution are included in order to show the behavior of the estimates.
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| 7. |
- Bolin, David, 1983, et al.
(författare)
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Weak convergence of Galerkin approximations for fractional elliptic stochastic PDEs with spatial white noise
- 2018
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Ingår i: BIT (Copenhagen). - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 58:4, s. 881-906
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Tidskriftsartikel (refereegranskat)abstract
- The numerical approximation of the solution to a stochastic partial differential equation with additive spatial white noise on a bounded domain is considered. The differential operator is assumed to be a fractional power of an integer order elliptic differential operator. The solution is approximated by means of a finite element discretization in space and a quadrature approximation of an integral representation of the fractional inverse from the Dunford–Taylor calculus. For the resulting approximation, a concise analysis of the weak error is performed. Specifically, for the class of twice continuously Fréchet differentiable functionals with second derivatives of polynomial growth, an explicit rate of weak convergence is derived, and it is shown that the component of the convergence rate stemming from the stochasticity is doubled compared to the corresponding strong rate. Numerical experiments for different functionals validate the theoretical results.
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| 8. |
- Breiten, Tobias, et al.
(författare)
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Residual-based iterations for the generalized Lyapunov equation
- 2019
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Ingår i: BIT Numerical Mathematics. - : Springer Netherlands. - 0006-3835 .- 1572-9125. ; 59:4, s. 823-852
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Tidskriftsartikel (refereegranskat)abstract
- This paper treats iterative solution methods for the generalized Lyapunov equation. Specifically, a residual-based generalized rational-Krylov-type subspace is proposed. Furthermore, the existing theoretical justification for the alternating linear scheme (ALS) is extended from the stable Lyapunov equation to the stable generalized Lyapunov equation. Further insights are gained by connecting the energy-norm minimization in ALS to the theory of H2-optimality of an associated bilinear control system. Moreover it is shown that the ALS-based iteration can be understood as iteratively constructing rank-1 model reduction subspaces for bilinear control systems associated with the residual. Similar to the ALS-based iteration, the fixed-point iteration can also be seen as a residual-based method minimizing an upper bound of the associated energy norm.
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| 9. |
- Cohen, David, et al.
(författare)
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Linear energy-preserving integrators for Poisson systems
- 2011
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Ingår i: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 51:1, s. 91-101
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Tidskriftsartikel (refereegranskat)abstract
- For Hamiltonian systems with non-canonical structure matrix a new class of numerical integrators is proposed. The methods exactly preserve energy, are invariant with respect to linear transformations, and have arbitrarily high order. Those of optimal order also preserve quadratic Casimir functions. The discussion of the order is based on an interpretation as partitioned Runge-Kutta method with infinitely many stages.
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| 10. |
- Cohen, David, et al.
(författare)
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Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions
- 2015
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Ingår i: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 55:3, s. 705-732
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Tidskriftsartikel (refereegranskat)abstract
- For trigonometric and modified trigonometric integrators applied to oscillatory Hamiltonian differential equations with one or several constant high frequencies, near-conservation of the total and oscillatory energies are shown over time scales that cover arbitrary negative powers of the step size. This requires non-resonance conditions between the step size and the frequencies, but in contrast to previous results the results do not require any non-resonance conditions among the frequencies. The proof uses modulated Fourier expansions with appropriately modified frequencies.
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