GPU-Accelerated 3D Mesh Deformation for Optimization Based on the Finite Element Method

This paper discusses a strategy for speeding up the mesh deformation process in the design-by-optimization of high-frequency components involving electromagnetic field simulations using the 3D finite element method (FEM). The mesh deformation is assumed to be described by a linear elasticity model of a rigid body; therefore, each time the shape of the device is changed, an auxiliary elasticity finite-element problem must be solved. In order to accomplish this in a very short time numerical integration and the solution of the resulting system of equations are performed using a graphics processing unit (GPU). The performance of the proposed algorithm is illustrated are verified using a complex example involving 3D FEM analysis of a dielectric-resonator filter