Collocation Trefftz Method for the Heat Conduction Issue in Irregular Domain with Non-Linear Boundary Condition

Abstract

Rules for nonlinear borders of irregular domain is the thorny issues when using analytical method for solving mathematical and physical equations. On the basis of solution in the form of separated variables, the border of arbitrary shape with non-orthogonal boundary will be separated into a limited number of discrete points, and then direct assignment for the form solution at each of the discrete points on the border according to boundary conditions, at every discrete points on the border can establish an equation. If the number of discrete points on the border is equal with truncated series after retained series, all coefficients of the form solution can be determined and the problem solved. This paper use Laplace equation as an example to illustrate Collocation Trefftz Method can solve certain steady heat conduction problems within irregular domain with non-linear border.