Communications on Applied Mathematics and Computation

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A Split-Step Predictor–Corrector Method for Space-Fractional Reaction–Diffusion Equations with Nonhomogeneous Boundary Conditions
Communications on Applied Mathematics and Computation - Tập 1 - Trang 525-544 - 2019
Kamran Kazmi, Abdul Khaliq
A split-step second-order predictor–corrector method for space-fractional reaction–diffusion equations with nonhomogeneous boundary conditions is presented and analyzed for the stability and convergence. The matrix transfer technique is used for spatial discretization of the problem. The method is shown to be unconditionally stable and second-order convergent. Numerical experiments are performed t...... hiện toàn bộ
Energy Stable Nodal DG Methods for Maxwell’s Equations of Mixed-Order Form in Nonlinear Optical Media
Communications on Applied Mathematics and Computation - - 2022
Maohui Lyu, Vrushali A. Bokil, Yingda Cheng, Fengyan Li
In this work, we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion, the instantaneous nonlinear cubic Kerr response, and the nonlinear delayed Raman molecular vibrational response. Unlike the first-order PDE-ODE governing equations considered previously in Bokil et al. (J Comput Phy...... hiện toàn bộ
The Perturbed Riemann Problem for a Geometrical Optics System
Communications on Applied Mathematics and Computation - Tập 5 Số 3 - Trang 1148-1179 - 2023
Shiwei Li, Hanchun Yang
Deep Energies for Estimating Three-Dimensional Facial Pose and Expression
Communications on Applied Mathematics and Computation - - Trang 1-25 - 2023
Jane Wu, Michael Bao, Xinwei Yao, Ronald Fedkiw
While much progress has been made in capturing high-quality facial performances using motion capture markers and shape-from-shading, high-end systems typically also rely on rotoscope curves hand-drawn on the image. These curves are subjective and difficult to draw consistently; moreover, ad-hoc procedural methods are required for generating matching rotoscope curves on synthetic renders embedded i...... hiện toàn bộ
On the Use of Monotonicity-Preserving Interpolatory Techniques in Multilevel Schemes for Balance Laws
Communications on Applied Mathematics and Computation - - Trang 1-23 - 2024
Antonio Baeza, Rosa Donat, Anna Martínez-Gavara
Cost-effective multilevel techniques for homogeneous hyperbolic conservation laws are very successful in reducing the computational cost associated to high resolution shock capturing numerical schemes. Because they do not involve any special data structure, and do not induce savings in memory requirements, they are easily implemented on existing codes and are recommended for 1D and 2D simulations ...... hiện toàn bộ
ADER Methods for Hyperbolic Equations with a Time-Reconstruction Solver for the Generalized Riemann Problem: the Scalar Case
Communications on Applied Mathematics and Computation - Tập 2 - Trang 369-402 - 2019
R. Demattè, V. A. Titarev, G. I. Montecinos, E. F. Toro
The ADER approach to solve hyperbolic equations to very high order of accuracy has seen explosive developments in the last few years, including both methodological aspects as well as very ambitious applications. In spite of methodological progress, the issues of efficiency and ease of implementation of the solution of the associated generalized Riemann problem (GRP) remain the centre of attention ...... hiện toàn bộ
Sequential Approximation of Functions in Sobolev Spaces Using Random Samples
Communications on Applied Mathematics and Computation - Tập 1 - Trang 449-466 - 2019
Kailiang Wu, Dongbin Xiu
We present an iterative algorithm for approximating an unknown function sequentially using random samples of the function values and gradients. This is an extension of the recently developed sequential approximation (SA) method, which approximates a target function using samples of function values only. The current paper extends the development of the SA methods to the Sobolev space and allows the...... hiện toàn bộ
The Hermite-Taylor Correction Function Method for Maxwell’s Equations
Communications on Applied Mathematics and Computation - - Trang 1-25 - 2023
Yann-Meing Law, Daniel Appelö
The Hermite-Taylor method, introduced in 2005 by Goodrich et al. is highly efficient and accurate when applied to linear hyperbolic systems on periodic domains. Unfortunately, its widespread use has been prevented by the lack of a systematic approach to implementing boundary conditions. In this paper we present the Hermite-Taylor correction function method (CFM), which provides exactly such a syst...... hiện toàn bộ
Preface
Communications on Applied Mathematics and Computation - - Trang 1-2 - 2023
Qing Nie, Chi-Wang Shu, Yulong Xing, Yong-Tao Zhang
Maximum-Principle-Preserving Local Discontinuous Galerkin Methods for Allen-Cahn Equations
Communications on Applied Mathematics and Computation - - 2022
Jian Du, Eric T. Chung, Yang Yang
Tổng số: 240   
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