The scalability of the matrices in direct Trefftz method in 2D Laplace problem

TL;DR

This paper investigates a property of matrices in the 2D Laplace problem using the direct Trefftz method, showing that matrix elements scale inversely with the domain size, with applications to capacitance extraction.

Contribution

It analytically proves a scalability property of matrices in the 2D Laplace problem using the direct Trefftz method, facilitating more efficient capacitance calculations.

Findings

Matrix elements are inversely proportional to the scalability factor.

The scalability property can be utilized in capacitance extraction algorithms.

Numerical results support the analytical proof.

Abstract

This paper presents an interesting property of the matrices that may be obtained with the use of direct Trefftz method. It is proved analytically for 2D Laplace problem that values of the elements of matrices describing the capacitance of two scaled domains are inversely proportional to the scalability factor. As an example of the application the capacitance extraction problem is chosen. Concise description of the algorithm in which the scalability property can be utilized is given. Furthermore some numerical results of the algorithm are presented.