Soft-field imaging methods, such as Optical Tomography (OT) and Electrical Impedance Tomography (EIT) have significant potential for medical imaging as they are non-invasive, portable and inexpensive. Possible clinical applications include epilepsy monitoring, cerebral stroke differentiation and screening for breast cancer. Recent advances in data acquisition instrumentation and image reconstru...

Due to improvements in computational resources, interest has recently increased in using implicit scheme for solving flow equations on 3D unstructured grids. However, most of the implicit schemes produce greater numerical diffusion error than their corresponding explicit schemes. This stems from the fact that in linearizing implicit fluxes, it is conventional to replace the Jacobian matrix in t...

AILU: A Preconditioner Based on the Analytic Factorization of the Elliptic Operator Martin J. Gander and Frederic Nataf Department of Mathematics, McGill University, Montreal, Canada and CMAP, CNRS UMR7641, Ecole Polytechnique, Palaiseau, France We investigate a new type of preconditioner for large systems of linear equations stemming from the discretization of elliptic symmetric partial differ...

A Newton-Krylov method is developed for the solution of the steady compressible NavierStokes equations using a Discontinuous Galerkin (DG) discretization on unstructured meshes. An element Line-Jacobi preconditioner is presented which solves a block tridiagonal system along lines of maximum coupling in the flow. An incomplete block-LU factorization (BlockILU(0)) is also presented as a precondit...

F11DNF Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. 1 Purpose F11DNF computes an incomplete LU factorization of a complex sparse non-Hermitian matrix, represented in coordinate storage format. This factorization may be used as a preconditioner in combination w...

This paper describes a domain-based multilevel block ILU preconditioner (BILUTM) for solving general sparse linear systems. This preconditioner combines a high accuracy incomplete LU factorization with an algebraic multilevel recursive reduction. Thus, in the first level the matrix is permuted into a block form using (block) independent set ordering and an ILUT factorization for the reordered m...

Due to improvements in computational resources, interest has recently increased in using implicit scheme for solving flow equations on 3D unstructured grids. However, most of the implicit schemes produce greater numerical diffusion error than their corresponding explicit schemes. This stems from the fact that in linearizing implicit fluxes, it is conventional to replace the Jacobian matrix in t...

For the iterative solutions of the integral equation methods employing the multilevel fast multipole algorithm (MLFMA), effective preconditioning techniques should be developed for robustness and efficiency. Preconditioning techniques for such problems can be broadly classified as fixed preconditioners that are generated from the sparse near-field matrix and variable ones that can make use of M...