Search results for "Fast BEM solver"
showing 9 items of 9 documents
Hierarchical adaptive cross approximation GMRES technique for solution of acoustic problems using the boundary element method
2009
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…
A fast BEM for the analysis of damaged structures with bonded piezoelectric sensors
2010
A fast boundary element method 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 computationa…
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.
Fast Solution of 3D Elastodynamic Boundary Element Problems by Hierarchical Matrices
2009
In this paper a fast solver for three-dimensional elastodynamic BEM problems formulated in the Laplace transform domain is presented, implemented and tested. The technique is based on the use of hierarchical matrices for the representation of the collocation matrix for each value of the Laplace parameter of interest 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. An original strategy for speeding up the overall analysis is presented and tested. The reported numerical results demonstrate the effectiveness of the technique.
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 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 fast hierarchical dual boundary element method for three-dimensional elastodynamic crack problems
2010
In this work a fast solver for large-scale three-dimensional elastodynamic crack problems is presented, implemented, and tested. The dual boundary element method in the Laplace transform domain is used for the accurate dynamic analysis of cracked bodies. The fast solution procedure is based on the use of hierarchical matrices for the representation of the collocation matrix for each computed value of the Laplace parameter. An ACA (adaptive cross approximation) algorithm is used for the population of the low rank blocks and its performance at varying Laplace parameters is investigated. A preconditioned GMRES is used for the solution of the resulting algebraic system of equations. The precond…
A fast dual boundary element method for 3D anisotropic crack problems
2009
In the present paper a fast solver for dual boundary element analysis of 3D anisotropic crack problems is formulated, implemented and tested. The fast solver is based on the use of hierarchical matrices for the representation of the collocation matrix. The admissible low rank blocks are computed by adaptive cross approximation (ACA). The performance of ACA against the accuracy of the adopted computational scheme for the evaluation of the anisotropic kernels is investigated, focusing on the balance between the kernel representation accuracy and the accuracy required for ACA. The system solution is computed by a preconditioned GMRES and the preconditioner is built exploiting the hierarchical …