| 1. |
- Aarao, J, et al.
(författare)
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Numerical implementation of the EDEM for modified Helmholtz BVPs on annular domains
- 2011
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Ingår i: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - : Elsevier Science B.V., Amsterdam.. - 0377-0427. ; 235:5, s. 1342-1353
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Tidskriftsartikel (refereegranskat)abstract
- In a recent paper by the current authors a new methodology called the Extended-Domain-Eigenfunction-Method (EDEM) was proposed for solving elliptic boundary value problems on annular-like domains. In this paper we present and investigate one possible numerical algorithm to implement the EDEM. This algorithm is used to solve modified Helmholtz BVPs on annular-like domains. Two examples of annular-like domains are studied. The results and performance are compared with those of the well-known boundary element method (BEM). The high accuracy of the EDEM solutions and the superior efficiency of the EDEM over the BEM, make EDEM an excellent alternate candidate to use in the animation industry, where speed is a predominant requirement, and by the scientific community where accuracy is the paramount objective.
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| 2. |
- Agram, Nacira, 1987-, et al.
(författare)
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Infinite horizon optimal control of forward–backward stochastic differential equations with delay
- 2014
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier. - 0377-0427 .- 1879-1778. ; 259:Part B, s. 336-349
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Tidskriftsartikel (refereegranskat)abstract
- We consider a problem of optimal control of an infinite horizon system governed by forward–backward stochastic differential equations with delay. Sufficient and necessary maximum principles for optimal control under partial information in infinite horizon are derived. We illustrate our results by an application to a problem of optimal consumption with respect to recursive utility from a cash flow with delay.
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| 3. |
- Bogers, J., et al.
(författare)
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A multiscale domain decomposition approach for chemical vapor deposition
- 2013
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Ingår i: Journal of Computational and Applied Mathematics. - Amsterdam, Netherlands : Elsevier. - 0377-0427 .- 1879-1778. ; 246, s. 65-73
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Tidskriftsartikel (refereegranskat)abstract
- We consider the process of chemical vapor deposition on a trenched Si substrate. To understand the process (including e.g. the layer conformality) at the trench scale (microscale), we need solutions at both the trench and reactor scales (macroscale). Due to the huge difference in size of these scales, straightforward numerical computations are very challenging. To overcome this difficulty, we consider a multiscale approach by introducing an intermediate scale (the mesoscale). We start with a time-continuous model describing the transport processes and then perform time discretization. At each time step, using the ideas of domain decomposition inspired from Lions (1988) [4], we provide iterative coupling conditions for these three different scales. Using a weak formulation for the time-discrete equations, we prove the convergence of this iterative scheme at each time step. The approach also provides an alternative proof for the existence of the solutions for the time-discrete formulation. (C) 2012 Elsevier B.V. All rights reserved.
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| 4. |
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| 5. |
- Bradshaw-Hajek, B H, et al.
(författare)
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A composite Level Set and Extended-Domain-Eigenfunction Method for simulating 2D Stokes flow involving a free surface
- 2013
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier. - 0377-0427 .- 1879-1778. ; 237:1, s. 389-402
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the Extended-Domain-Eigenfunction-Method (EDEM) is combined with the Level Set Method in a composite numerical scheme for simulating a moving boundary problem. The liquid velocity is obtained by formulating the problem in terms of the EDEM methodology and solved using a least square approach. The propagation of the free surface is effected by a narrow band Level Set Method. The two methods both pass information to each other via a bridging process, which allows the position of the interface to be updated. The numerical scheme is applied to a series of problems involving a gas bubble submerged in a viscous liquid moving subject to both an externally generated flow and the influence of surface tension.
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| 6. |
- Chaudhry, Q. A., et al.
(författare)
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Surface reactions on the cytoplasmatic membranes - Mathematical modeling of reaction and diffusion systems in a cell
- 2014
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier BV. - 0377-0427 .- 1879-1778. ; 262, s. 244-260
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Tidskriftsartikel (refereegranskat)abstract
- A human cell consists schematically of an outer cellular membrane, a cytoplasm containing a large number of organelles (mitochondria, endoplasmatic reticulum etc.), a nuclear membrane and finally the cellular nucleus containing DNA. The organelles create a complex and dense system of membranes or sub-domains throughout the cytoplasm. The mathematical description leads to a system of reaction-diffusion equations in a complex geometrical domain, dominated by thin membranous structures with similar physical and chemical properties. In a previous model, we considered only spatially distributed reaction and diffusion processes. However, from experiments it is known that membrane bound proteins play an important role in the metabolism of certain substances. In the present paper we develop a homogenization strategy which includes both volume and surface reactions. The homogenized system is a reaction-diffusion system in the cytoplasm which is coupled to the surrounding cell components by correspondingly modified transfer conditions. The approach is verified by application to a system modeling the cellular uptake and intracellular dynamics of carcinogenic polycyclic aromatic hydrocarbons.
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| 7. |
- Cohen, David, et al.
(författare)
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Geometric finite difference schemes for the generalized hyperelastic-rod wave equation
- 2011
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier BV. - 0377-0427 .- 1879-1778. ; 235:8, s. 1925-1940
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Tidskriftsartikel (refereegranskat)abstract
- Geometric integrators are presented for a class of nonlinear dispersive equations which includes the Camassa-Holm equation, the BBM equation and the hyperelastic-rod wave equation. One group of schemes is designed to preserve a global property of the equations: the conservation of energy; while the other one preserves a more local feature of the equations: the multi-symplecticity. (C) 2010 Elsevier B.V. All rights reserved.
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| 8. |
- Doersek, Philipp, et al.
(författare)
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High order splitting schemes with complex timesteps and their application in mathematical finance
- 2014
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier BV. - 0377-0427. ; 262, s. 234-243
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Tidskriftsartikel (refereegranskat)abstract
- High order splitting schemes with complex timesteps are applied to Kolmogorov backward equations stemming from stochastic differential equations in the Stratonovich form. in the setting of weighted spaces, the necessary analyticity of the split semigroups can easily be proved. A numerical example from interest rate theory, the CIR2 model, is considered. The numerical results are robust for drift-dominated problems and confirm our theoretical results. (C) 2013 Elsevier B.V. All rights reserved.
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| 9. |
- Erickson, Brittany A., et al.
(författare)
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Stable, high order accurate adaptive schemes for long time, highly intermittent geophysics problems
- 2014
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier. - 0377-0427 .- 1879-1778. ; 271, s. 328-338
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Tidskriftsartikel (refereegranskat)abstract
- Many geophysical phenomena are characterized by properties that evolve over a wide range of scales which introduce difficulties when attempting to model these features in one computational method. We have developed a high-order finite difference method for the elastic wave equation that is able to efficiently handle varying temporal and spatial scales in a single, stand-alone framework. We apply this method to earthquake cycle models characterized by extremely long interseismic periods interspersed with abrupt, short periods of dynamic rupture. Through the use of summation-by-parts operators and weak enforcement of boundary conditions we derive a provably stable discretization. Time stepping is achieved through the implicit θθ-method which allows us to take large time steps during the intermittent period between earthquakes and adapts appropriately to fully resolve rupture.
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| 10. |
- Frentz, Marie, 1980-, et al.
(författare)
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Adaptive stochastic weak approximation of degenerate parabolic equations of Kolmogorov type
- 2010
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier. - 0377-0427 .- 1879-1778. ; 234:1, s. 146-164
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Tidskriftsartikel (refereegranskat)abstract
- Degenerate parabolic equations of Kolmogorov type occur in many areas of analysis and applied mathematics. In their simplest form these equations were introduced by Kolmogorov in 1934 to describe the probability density of the positions and velocities of particles but the equations are also used as prototypes for evolution equations arising in the kinetic theory of gases. More recently equations of Kolmogorov type have also turned out to be relevant in option pricing in the setting of certain models for stochastic volatility and in the pricing of Asian options. The purpose of this paper is to numerically solve the Cauchy problem, for a general class of second order degenerate parabolic differential operators of Kolmogorov type with variable coefficients, using a posteriori error estimates and an algorithm for adaptive weak approximation of stochastic differential equations. Furthermore, we show how to apply these results in the context of mathematical finance and option pricing. The approach outlined in this paper circumvents many of the problems confronted by any deterministic approach based on, for example, a finite-difference discretization of the partial differential equation in itself. These problems are caused by the fact that the natural setting for degenerate parabolic differential operators of Kolmogorov type is that of a Lie group much more involved than the standard Euclidean Lie group of translations, the latter being relevant in the case of uniformly elliptic parabolic operators.
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