Related papers: Simulation of Wave Equation on Manifold using DEC
In this paper, the method of discrete exterior calculus for numerically solving Maxwell's equations in space manifold and the time is discussed, which is a kind of lattice gauge theory. The analysis of its stable condition and error is also…
The Westervelt equation is a model for the propagation of finite amplitude ultrasound. The method of discrete exterior calculus can be used to solve this equation numerically. A significant advantage of this method is that it can be used to…
To predict the heat diffusion in a given region over time, it is often necessary to find the numerical solution for heat equation. With the techniques of discrete differential calculus, we propose two unconditional stable numerical schemes…
Maxwell's equations can be solved numerically in space manifold and the time by discrete exterior calculus as a kind of lattice gauge theory.Since the stable conditions of this method is very severe restriction, we combine the implicit…
We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
We derive new, explicit representations for the solution to the scalar wave equation in the exterior of a sphere, subject to either Dirichlet or Robin boundary conditions. Our formula leads to a stable and high-order numerical scheme that…
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain…
The question of what conditions should be set at the nodes of a discrete graph for the wave equation with discrete time is investigated. The variational method for the derivation of these conditions is used. A parallel with the continuous…
In this paper, we consider the classical wave equation with time-dependent, spatially multiscale coefficients. We propose a fully discrete computational multiscale method in the spirit of the localized orthogonal decomposition in space with…
A numerical method is proposed for computing time-periodic and relative time-periodic solutions in dissipative wave systems. In such solutions, the temporal period, and possibly other additional internal parameters such as the propagation…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…
Time-dependent wave equations represent an important class of partial differential equations (PDE) for describing wave propagation phenomena, which are often formulated over unbounded domains. Given a compactly supported initial condition,…
In the last years, several quantum algorithms that try to address the problem of partial differential equation solving have been devised. On one side, "direct" quantum algorithms that aim at encoding the solution of the PDE by executing one…
This work is thought as an operative guide to discrete exterior calculus (DEC), but at the same time with a rigorous exposition. We present a version of (DEC) on cubic cell, defining it for discrete manifolds. An example of how it works, it…
Discretization is a fundamental step in numerical analysis for the problems described by differential equations, and the difference between the continuous model and discrete model is one of the most important problems. In this paper, we…
In this paper we consider a singular wave equation with distributional and more singular non-distributional coefficients and develop tools and techniques for the phase-space analysis of such problems. In particular we provide a detailed…
A new numerical domain decomposition method is proposed for solving elliptic equations on compact Riemannian manifolds. The advantage of this method is to avoid global triangulations or grids on manifolds. Our method is numerically tested…
A conservative primitive variable discrete exterior calculus (DEC) discretization of the Navier-Stokes equations is performed. An existing DEC method (Mohamed, M. S., Hirani, A. N., Samtaney, R. (2016). Discrete exterior calculus…