Object-free adaptive meshing in highly heterogeneous 3-D domains

Abstract

Traditional approaches to the generation of finite element meshes are well suited for modeling the homogeneous or mildly heterogeneous domains presented by man-made objects, but are difficult to apply to the complex 3-D domains encountered in some biomedical applications. In this paper, we describe an adaptive algorithm that automates the modeling of these domains. The method differs from traditional approaches in that no explicit description is required of the boundaries between objects with dissimilar material properties. The algorithm uses images of the tissue class to build irregular meshes, and continuity is enforced by constraining the solution at irregular nodes. Local estimates of the error in the flux solution are used to refine the mesh. For an analytic problem with a rapid change along a spherical boundary, the adaptive method converges to a 1% voltage error using 25% of the degrees of freedom required by a uniform refinement, and to a 5% voltage gradient error using 11% of the degrees of freedom. For a defibrillation model in a pig thorax, the voltage gradient solution in the ventricles of the heart converges to within 5% of a uniform mesh solution using less than 8% of the memory and processing resources required by a uniform mesh, which has been the only practical alternative for subject-specific modeling.