Simulation of Wave Equation on Manifold using DEC

2009/09/28 by Zheng Xie, Yujie Ma, Xie, Zheng +1
Computer Science · Engineering · #03G10 #52C99 #81T75 #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #Computer Graphics and Visualization Techniques #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.0909.5008

openalex publication_date 2009/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The classical numerical methods play important roles in solving wave equation, e.g. finite difference time domain method. However, their computational domain are limited to flat space and the time. This paper deals with the description of discrete exterior calculus method for numerical simulation of wave equation. The advantage of this method is that it can be used to compute equation on the space manifold and the time. The analysis of its stable condition and error is also accomplished.

Related

• Computation of Maxwell's equations on Manifold using DEC
• Westervelt Equation Simulation on Manifold using DEC
• Two unconditional stable schemes for simulation of heat equation on manifold using DEC
• Computation of Maxwell's equations on manifold using implicit DEC scheme
• An A-Phi Formulation Solver in Electromagnetics Based on Discrete Exterior Calculus