0000000000612847
AUTHOR
M. H. Aliabadi
A fast 3D BEM for anisotropic elasticity based on hierarchical matrices
In this paper a fast solver for three-dimensional anisotropic elasticity BEM problems is developed. The technique is based on the use of hierarchical matrices for the representation of the collocation matrix and uses a preconditioned GMRES for the solution of the algebraic system of equations. The preconditioner is built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format. The application of hierarchical matrices to the BEM solution of anisotropic elasticity problems has been numerically demonstrated highlighting both accuracy and efficiency leading to almost linear computational complexity.
Hierarchical adaptive cross approximation GMRES technique for solution of acoustic problems using the boundary element method
In this paper a new Rapid Acoustic Boundary Element Method (RABEM) is presented using a Hierarchical GMRES solver for 3D acoustic problems. The Adaptive Cross Approximation is used to generate both the system matrix and the right hand side vector. The ACA is also used to evaluate the potential and the particle velocity values at selected internal points. Two different GMRES solution strategies (without preconditioner and with a block diagonal preconditioner) are developed and tested for low and high frequency problems. Implementation of different boundary conditions (i.e. Dirichlet, Neumann and mixed Robin) is also described. The applications presented include the problem of noise acting on…