Shape Optimization of the Stokes Eigenvalue Problem
Jiajie Li, Shengfeng Zhu
Abstract
.We consider solving the Stokes eigenvalue optimization problem. Distributed and boundary types of Eulerian derivatives are derived from shape calculus. A priori error estimates for finite element discretizations of both shape gradients are shown. The approximate distributed shape gradient has better convergence and is used in numerical algorithms. We propose a single-grid algorithm and a two-grid algorithm for Stokes eigenvalue optimization. Numerical results are presented to verify theory and show effectiveness and efficiency of the algorithms proposed.Keywordsshape optimizationStokes eigenvaluedistributed shape gradientmixed finite elementerror estimateMSC codes49Q1265K1065N3065N25
Topics & Concepts
MathematicsEigenvalues and eigenvectorsGridShape optimizationConvergence (economics)Finite element methodStokes flowApplied mathematicsEulerian pathA priori and a posterioriBoundary (topology)Divide-and-conquer eigenvalue algorithmMathematical optimizationMathematical analysisAlgorithmGeometryPhilosophyEpistemologyEconomicsLagrangianQuantum mechanicsEconomic growthPhysicsThermodynamicsFlow (mathematics)Topology Optimization in EngineeringAdvanced Numerical Analysis TechniquesAdvanced Numerical Methods in Computational Mathematics