Time-domain boundary integral equation modeling of heat transmission problems

TL;DR

This paper presents a novel numerical approach using convolution quadrature boundary element methods for modeling heat transmission problems, providing improved error estimates and stability analysis over traditional methods.

Contribution

It introduces a new theoretical framework for error analysis and stability in time-dependent heat transmission modeling using boundary element methods.

Findings

Enhanced error estimates compared to traditional Laplace domain methods

Stability achieved through semigroup theory in spatial discretization

Convergence demonstrated via functional calculus in fully discrete schemes

Abstract

This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoretical development into the error analysis of the numerical scheme. Semigroup theory is applied to obtain stability in spatial semidiscrete scheme. Functional calculus is employed to yield convergence in the fully discrete scheme. In comparison to the traditional Laplace domain approach, we show our approach gives better estimates.