Implicit finite difference schemes for the magnetic induction equations
U. Koley
TL;DR
This paper develops high-order, stable finite difference schemes for magnetic induction equations using SBP operators and SAT boundary conditions, demonstrating their effectiveness through numerical experiments.
Contribution
The paper introduces a novel combination of SBP operators and SAT techniques for stable, high-order finite difference schemes for magnetic induction equations.
Findings
Schemes are stable and high-order accurate
Numerical experiments confirm theoretical properties
Effective for initial-boundary value problems
Abstract
We describe high order accurate and stable fully-discrete finite difference schemes for the initial-boundary value problem associated with the magnetic induction equations. These equations model the evolution of a magnetic field due to a given velocity field. The finite difference schemes are based on Summation by Parts (SBP) operators for spatial derivatives and a Simultaneous Approximation Term (SAT) technique for imposing boundary conditions. We present various numerical experiments that demonstrate both the stability as well as high order of accuracy of the schemes
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Numerical methods for differential equations · Electromagnetic Simulation and Numerical Methods