Search results for "hierarchical matrices"
showing 7 items of 7 documents
On the accuracy of the fast hierarchical DBEM for the analysis of static and dynamic crack problems
2010
In this paper the main features of a fast dual boundary element method based on the use of hierarchical matrices and iterative solvers are described and its effectiveness for fracture mechanics problems, both in the static and dynamic case, is demonstrated. The fast solver is built by representing the collocation matrix in hierarchical format and by using a preconditioned GMRES for the solution of the algebraic system. The preconditioner is computed in hierarchical format by LU decomposition of a coarse hierarchical representation of the collocation matrix. The method is applied to elastostatic problems and to elastodynamic cases represented in the Laplace transform domain. The application …
A fast 3D BEM for anisotropic elasticity based on hierarchical matrices
2008
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.
A fast BEM model for 3D elastic structures with attached piezoelectric sensors
2009
A fast boundary element model for the analysis of three-dimensional solids with cracks and adhesively bonded piezoelectric patches, used as strain sensors, is presented. The piezoelectric sensors, as well as the adhesive layer, are modeled using a 3D state space finite element approach. The piezoelectric patch model is formulated taking into account the full electro-mechanical coupling and embodying the suitable boundary conditions and it is eventually expressed in terms of the interface variables, to allow a straightforward coupling with the underlying host structure, which is modeled through a 3D dual boundary element method, for accurate analysis of cracks. The technique is computational…
A fast 3D dual boundary element method based on hierarchical matrices
2008
AbstractIn this paper a fast solver for three-dimensional BEM and DBEM 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. Special algorithms are developed to deal with crack problems within the context of DBEM. The structure of DBEM matrices has been efficiently exploited and it has been demonstrated that, since the cracks form only small parts of the whole structure, the use of hierarchical matrices can be particula…
A fast BEM for the analysis of plates with bonded piezoelectric patches
2010
In this paper a fast boundary element method for the elastodynamic analysis of 3D structures with bonded piezoelectric patches is presented. The elastodynamic analysis is performed in the Laplace domain and the time history of the relevant quantities is obtained by inverse Laplace transform. The bonded patches are modelled using a semi-analytical state-space variational approach. The computational features of the technique, in terms of required storage memory and solution time, are improved by a fast solver based on the use of hierarchical matrices. The presented numerical results show the potential of the technique in the study of structural health monitoring (SHM) systems.
A hierarchical-ACA technique for large-scale acoustic simulations: complex geometries with sound adsorbent materials
2012
In this paper a boundary element approach for acoustic simulations based on the hierarchical-matrix format coupled with the adaptive cross approximation (ACA) algorithm and a hierarchical GMRES solver is presented. The cluster tree is generated using preliminary considerations of the prescribed boundary conditions. An improved ACA algorithm, applied, separately, to Neumann, Dirichlet and mixed Robin conditions, is described. Numerical results are presented to show the new approach to be up to 50% faster than conventional ACA approach.