Solitary Wave Benchmarks in Magma Dynamics

Authors:
G. Simpson;M. Spiegelman
Affiliations:
Department of Mathematics, University of Toronto, Toronto, Canada;Department of Applied Physics & Applied Mathematics, Department of Earth & Environmental Sciences, Columbia University, New York, USA
Venue:
Journal of Scientific Computing
Year:
2011

Citing 9
Cited 0

Sinc methods for quadrature and differential equations

Sinc methods for quadrature and differential equations
Efficient management of parallelism in object-oriented numerical software libraries

Modern software tools for scientific computing
Summary of Sinc numerical methods

Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
A MATLAB differentiation matrix suite

ACM Transactions on Mathematical Software (TOMS)
Sinc numerical solution for solitons and solitary waves

Journal of Computational and Applied Mathematics
Convergence of Petviashvili's Iteration Method for Numerical Approximation of Stationary Solutions of Nonlinear Wave Equations

SIAM Journal on Numerical Analysis
A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity

Journal of Computational Physics
On the Galerkin and collocation methods for two-point boundary value problems using sinc bases

Computers & Mathematics with Applications
Nonlinear models and problems in applied sciences from differential quadrature to generalized collocation methods

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a model problem for benchmarking codes that investigate magma migration in the Earth's interior. This system retains the essential features of more sophisticated models, yet has the advantage of possessing solitary wave solutions. The existence of such exact solutions to the nonlinear problem make it an excellent benchmark problem for combinations of solver algorithms. In this work, we explore a novel algorithm for computing high quality approximations of the solitary waves in 1-, 2- and 3 dimensions and use them to benchmark a semi-Lagrangian Crank-Nicolson scheme for a finite element discretization of the time dependent problem.