The numerical solution of partial differential equations frequently requires the solution of large and sparse linear systems. Using generic programming techniques like in C++ one can create solver libraries that allow efficient realization of “fine grained interfaces”, i. e. with functions consisting only of a few lines, like access to individual matrix entries. This prevents code replication a...

This paper presents a fast iterative solver for Lippmann-Schwinger equation for highfrequency waves scattered by a smooth medium with a compactly supported inhomogeneity. The solver is based on the sparsifying preconditioner [63] and a domain decomposition approach similar to the method of polarized traces [64]. The iterative solver has two levels, the outer level in which a sparsifying precond...

Statistical computed tomography (CT) image reconstruction usually requires solving a very large-scale convex optimization problem. The iterative solver for CT reconstruction suffers from slow converging speed and high computational cost in projections and backprojections. The goal for this project is to accelerate the iterative solver using the Alternating Direction Method of Multiplier (ADMM) ...

We combine model-based testing and mutation testing to automatically generate a test suite that achieves a high mutation adequacy score. The original model representing the system under test is mutated. To generate test cases that detect whether a modelled fault has been implemented, we perform a refinement check between the original and the mutated models. Action systems serve as formal models...

This paper provides an outline of the Gabbay-Rodrigues Iterative Solver (GRIS). The solver can be used in decision and enumeration problems of the grounded and preferred semantics.

Using the time direction in evolution problems for parallelization is an active field of research. Most of these methods are iterative, see for example the parareal algorithm analyzed in [3], a variant that became known under the name PFASST [10], and waveform relaxation methods based on domain decomposition [5, 4], see also [1] for a method called RIDC. Direct time parallel solvers are much mo...

Coupled 3D-1D problems arise in many practical applications, an attempt to reduce the computational burden simulations where cylindrical inclusions with a small section are embedded much larger domain. Nonetheless resolution of such can be non trivial, both from mathematical and geometrical standpoint. Indeed coupling requires operate standard function spaces, and, also, simulation geometries c...

We discuss the design and implementation of a suite of functions for solving symmetric indefinite linear systems associated with mixed approximation of systems of PDEs. The novel feature of our iterative solver is the incorporation of error control in the natural “energy” norm in combination with an a posteriori estimator for the PDE approximation error. This leads to a robust and optimally eff...