Extended smoothed boundary method for solving partial differential equations with general boundary conditions on complex boundaries
Journal
Modelling and Simulation in Materials Science and Engineering
Journal Volume
20
Journal Issue
7
Date Issued
2012
Author(s)
Abstract
In this paper, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A continuous function, the domain parameter, is used to modify the original differential equations such that the equations are solved in the region where a domain parameter takes a specified value while boundary conditions are imposed on the region where the value of the domain parameter varies smoothly across a short distance. The mathematical derivations are straightforward and applicable to a wide variety of partial differential equations. To demonstrate the general applicability of the approach, we provide four examples herein: (1) the diffusion equation with both Neumann and Dirichlet boundary conditions;
Type
journal article