Séance Séminaire

Séminaire ACSIOM

Solving Boundary Element methods with an iterative solver: incorporation of inequality constraints and optimizations. Applications to forward modeling, linear and non-linear inversion.

Boundary Element Methods (BEM) are more and more used for numerical simulations because of the easy way of describing and building a model. However, compare to Finite Element Method (FEM), the resulting system matrix is large and dense. Consequently, the problems of memory as well as the time needed to invert the system become non negligible. Furthermore, the incorporation of inequality constraints can increase the size of the system, and a new method has to be developed to treat all these problems in one go. We will present the advantages of an iterative solver for BEM in term of memory management and saving, optimizations, model complexity and parallelization on multi-core processors. A new method for describing inequality constraints is also presented, which does not increase the size of the system and does not have any drawback onto the convergence. Finally, before concluding, we will present a linear-inverse method applied on non-structured meshes using the same BEM formulation and a direct regularized constrained least squares approach. This, in order to expose the problems that we have in terms of regularization of the iterative version. The non-linear inversion is finally considered as a future development.