A time–dependent FEM-BEM coupling method for fluid–structure interaction in 3d

Abstract

We consider the well-posedness and a priori error estimates of a 3d FEM-BEM coupling method for fluid-structure interaction in the time domain. For an elastic body immersed in a fluid, the exterior linear wave equation for the fluid is reduced to an integral equation on the boundary involving the Poincaré-Steklov operator. The resulting problem is solved using a Galerkin boundary element method in the time domain, coupled to a finite element method for the Lamé equation inside the elastic body. Based on ideas from the timeindependent coupling formulation, we obtain an a priori error estimate and discuss the implementation of the proposed method. Numerical experiments illustrate the performance of our scheme for model problems.

Space‐time stochastic Galerkin boundary elements for acoustic scattering problems

“…Both space‐time Galerkin and convolution quadrature methods have been developed, see References 20–22 for an overview. Recent developments in the directions of the current work include stable formulations, 23–25 efficient discretizations, 26–31 compression of the dense matrices 32,33 as well as complex coupled and interface problems 34–41 …”

“…Recent developments in the directions of the current work include stable formulations, [23][24][25] efficient discretizations, [26][27][28][29][30][31] compression of the dense matrices 32,33 as well as complex coupled and interface problems. [34][35][36][37][38][39][40][41] To be specific, the method presented here reduces stochastic boundary value problems for the exterior acoustic wave equation to integral equations on the boundary of the computational domain. Using a polynomial chaos expansion of the random variables, a high-dimensional integral equation is obtained which is then discretized by a Galerkin method in space and time.…”

A SFBEM–FEM coupling method for solving crack problems based on Erdogan fundamental solutions

“…Therefore, in order to make full use of the unique advantage of BEM in dealing with the singular behaviour at crack tips and the superior flexibility of FEM in modelling complex structures and boundary conditions, several researchers proposed the BEM-FEM coupling methods to solve complex crack problems [15][16][17][18][19][20]. Actually, the BEM-FEM coupling techniques stem from the pioneering work of Zienkiewicz et al [21] and Brebbia and Georgiou [22], and now have appeared in the areas of flexoelectricity [23], vibroacoustic response [24], fluid-structure interaction [25] and soil-structure interaction [26], among others. Note that, for crack problems thus far, the BEM formulation for the BEM subdomain containing cracks has been established using the non-crack Kelvin fundamental solutions, and therefore, one also needs to consider the stress boundary conditions on crack surfaces and employ special crack-tip boundary elements to reflect the singular behaviour, which makes it inconvenient to calculate the SIFs at crack tips, even if the coupled BEM-FEM procedure has been adopted.…”