An Isogeometric Tearing and Interconnecting method for conforming discretizations of the biharmonic problem

TL;DR

This paper introduces an IETI-DP domain decomposition method tailored for conforming isogeometric discretizations of the biharmonic problem, providing theoretical analysis and numerical validation of its effectiveness.

Contribution

It develops a novel IETI-DP solver specifically designed for biharmonic problems discretized with multi-patch isogeometric analysis, including condition number estimates.

Findings

The method achieves stable and efficient solutions for biharmonic problems.

Numerical results confirm the theoretical condition number estimates.

The approach is suitable for two-dimensional smooth geometries.

Abstract

We propose and analyze a domain decomposition solver for the biharmonic problem. The problem is discretized in a conforming way using multi-patch Isogeometric Analysis. As first step, we discuss the setup of a sufficiently smooth discretization space. We focus on two dimensional computational domains that are parameterized with sufficiently smooth geometry functions. As solution technique, we use a variant of the Dual-Primal Finite Element Tearing and Interconnecting method that is also known as Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) method in the context of Isogeometric Analysis. We present a condition number estimate and illustrate the behavior of the proposed method with numerical results.