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In this paper, using an optimize-then-discretize approach, we address the numerical solution of two Fraction Partial Differential Equation constrained optimization problems: the Fractional Advection Dispersion Equation (FADE) and the two-dimensional semilinear Riesz Space Fractional Diffusion equation . Both a theoretical and experimental analysis of the problem is carried out. The algorithmic framework is based on the L-BFGS method coupled with a Krylov subspace solver. A suitable preconditioning strategy by approximate inverses is taken into account. Graphics Processing Unit (GPU) accelerator is used in the construction of the preconditioners. The numerical experiments are performed with benchmarked software/libraries enforcing the reproducibility of the results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose a simple meshless method of fundamental solutions (MFS) for detecting a sound-soft scatterer embedded in a host acoustic homogeneous medium from the measurement of the far-field pattern of the scattered wave for only one incoming direction. Further, when this measurement is contaminated with noise, we augment the MFS with a nonlinear constrained regularized minimization for obtaining a stable numerical solution of the inverse problem. Numerical results are presented and discussed. [Copyright &y& Elsevier]

Abstract: In this paper, a new line search filter algorithm for equality constrained optimization is presented. The approach belongs to the class of inexact Newton-like methods. It can also be regarded as an inexact version of generic sequential quadratic programming (SQP) methods. The trial step is obtained by truncatedly solving the primal–dual system based on any robust and efficient linear system solver. Practical termination tests for the linear system solver are established to ensure global convergence. Preliminary numerical results demonstrate the approach is potentially useful. [Copyright &y& Elsevier]

Abstract: We propose an unstaggered, non-oscillatory, second-order accurate central scheme for approximating the solution of general hyperbolic systems in one and two space dimensions, and in particular for estimating the solution of ideal magnetohydrodynamic problems and shallow water magnetohydrodynamic problems. In contrast with standard central schemes that evolve the numerical solution on two staggered grids at consecutive time steps, the method we propose evolves the numerical solution on a single unique grid, and avoids the resolution of the Riemann problems arising at the cell interfaces thanks to a layer of ghost staggered cells implicitly used while updating the numerical solution on the control cells. To satisfy the divergence-free constraint of the magnetic field/flux in the numerical solution of ideal/shallow water magnetohydrodynamic problems, we adapt Evans and Hawley''s constrained transport method to our unstaggered base scheme and use it to correct the magnetic field/flux components at the end of each time step. The resulting method is used to solve classical ideal/shallow water magnetohydrodynamic problems; the obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the efficiency and the potential of the proposed method. [Copyright &y& Elsevier]