Hybridized Isogeometric Method for Elliptic Problems on CAD Surfaces with Gaps

TL;DR

This paper introduces a hybridized isogeometric method for solving elliptic PDEs on CAD surfaces with gaps, utilizing a 3D mesh and stabilization techniques to handle complex geometries effectively.

Contribution

The paper presents a novel hybridization approach with normal stabilization for elliptic problems on CAD surfaces with gaps, including error analysis and practical implementation strategies.

Findings

Error estimates are established for the method.

Numerical examples demonstrate accuracy on complex CAD models.

The approach effectively handles gaps and overlaps in CAD patches.

Abstract

We develop a method for solving elliptic partial differential equations on surfaces described by CAD patches that may have gaps/overlaps. The method is based on hybridization using a three-dimensional mesh that covers the gap/overlap between patches. Thus, the hybrid variable is defined on a three-dimensional mesh, and we need to add appropriate normal stabilization to obtain an accurate solution, which we show can be done by adding a suitable term to the weak form. In practical applications, the hybrid mesh may be conveniently constructed using an octree to efficiently compute the necessary geometric information. We prove error estimates and present several numerical examples illustrating the application of the method to different problems, including a realistic CAD model.