The Perfect Laplace Operator for Non-Trivial Boundaries
S. Hauswirth
TL;DR
This paper develops a method to analytically and numerically compute the perfect fixed-point Laplace operator for complex boundary shapes, aiding in solving the Poisson equation more accurately.
Contribution
It introduces a novel approach to derive the classically perfect Laplace operator for non-trivial boundaries using RG methods, with a practical parametrization for PDE solutions.
Findings
Analytical and numerical calculation of the perfect Laplace operator for complex boundaries.
A parametrization enabling practical application to solve the Poisson equation.
Demonstration of improved discretization accuracy for non-trivial boundary shapes.
Abstract
The application of Renormalization Group (RG) methods to find perfect discretizations of partial differential equations is a promising but little investigated approach. We calculate the classically perfect fixed-point Laplace operator for boundaries of non-trivial shape analytically and numerically and present a parametrization that can be used for solving the Poisson equation.
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.