Jinsil Lee : Multivariate Spline Method for Solving Monge-Ampere Equation

Posted by Ian Tobasco , part of the Analysis and Applied Mathematics Seminar.

At

April 10, 2023, 4 p.m.

In

1227 SEO

Abstract

In this talk, I will give a brief introduction to a trivariate spline collocation method for solving the Dirichlet problem of the 3D elliptic Monge-Ampère equation. Specifically, I will explain the spline collocation method introduced in [SIAM J. Numerical Analysis, 2405-2434,2022] to numerically solve iterative Poisson equations, and incorporate an averaged algorithm to ensure convergence of the iterations. Furthermore, I present various computational results, including testing known convex and non-convex solutions over convex and non-convex domains to demonstrate the efficiency and effectiveness of the method.