Speaker
Manuel Solano, Universidad de Concepción
Abstract
In 2009, Cockburn, Reitich and Gupta, presented a novel idea to numerically solve one dimensional boundary value problems by considering a computational domain not necessarily fitting the true domain. It was based on the fundamental theorem of calculus that provides an explicit representation of the trace of the solution in the computational boundary in terms of two quantities: the prescribed boundary data in the true domain and the integral of the derivative of the solution. This methodology was then extended to two and three dimensional problems, where the Dirichlet boundary data is transferred from the true boundary to the computational domain along segments called transfer paths. Since then, the Transfer Path Method (TPM) has been applied to a variety of problems, originating high order unfitted numerical methods to solve partial differential equations, mostly in the context of hybridizable discontinuous Galerkin methods, but also for mixed finite elements.
This talk is devoted to providing an overview of the TPM, from its origin in 2009 to current developments, by showing its features, capabilities and limitations. In addition, applications of the TPM to perform simulations in plasma physics and shape optimization will be presented.