The sideways parabolic equation (SPE) is a model of the problem of determining the temperature on the surface of a body from the interior measurements. Mathematically it can be formulated as a noncharacteristic Cauchy problem for a parabolic partial differential equation. This problem is severely ill-posed in an L2 setting. We use a preconditioned generalized minimum residual method (GMRES) to ...

The Poisson-Boltzmann model is an effective and popular approach for modeling solvated biomolecules in continuum solvent with dissolved electrolytes. In this paper, we report our recent work developing a Galerkin boundary integral method solving the (PB) equation. solver has combined advantages accuracy, efficiency, memory usage as it applies well-posed formulation to circumvent many numerical ...

In this paper we present an electric field volume integral equation approach to simulate surface plasmon propagation along metal/dielectric interfaces. Metallic objects embedded in homogeneous dielectric media are considered. Starting point is a so-called weak-form of the electric field integral equation. This form is discretized on a uniform tensorproduct grid resulting in a system matrix whos...

In this paper we detail a fast, fully-coupled, partitioned fluid–structure interaction (FSI) scheme. For the incompressible fluid, new fractional-step algorithms are proposed which make possible the fully implicit, but matrixfree, parallel solution of the entire coupled fluid–solid system. These algorithms include artificial compressibility pressure-poisson solution in conjunction with upwind v...

We propose a general algorithm for solving a n×n nonsingular linear system Ax = b based on iterative refinement with three precisions. The working precision is combined with possibly different precisions for solving for the correction term and for computing the residuals. Via rounding error analysis of the algorithm we derive sufficient conditions for convergence and bounds for the attainable n...

We present a parallel Schwarz type domain decomposition preconditioned recycling Krylov subspace method for the numerical solution of stochastic indefinite elliptic equations with two random coefficients. Karhunen-Loève expansions are used to represent the stochastic variables and the stochastic Galerkin method with double orthogonal polynomials is used to derive a sequence of uncoupled determi...

We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media, with online parallel complexity that scales optimally as O(L ), where N is the number of volume unknowns, and L is the number of processors, as long as L grows at most like a small fractional power of N . The solver decomposes the domain into layers, and uses transmission conditions in boundary int...

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...

Abstract We consider the space-time discretization of diffusion equation, using an isogeometric analysis (IgA) approximation in space and a discontinuous Galerkin (DG) time. Drawing inspiration from former spectral analysis, we propose for resulting linear system multigrid preconditioned GMRES method, which combines with standard acting only space. The performance proposed solver is illustrated...