Channel coding aims to minimize errors that occur during the transmission of digital information from one place to another. Low–density parity–check (LDPC) codes can detect and correct transmission errors if one encodes the original information by adding redundant bits. In practice, heuristic iterative decoding algorithms are used to decode the received vector. However, these algorithms may fai...

A highly parallelizable domain decomposition solution technique for adaptive hp finite element methods is developed. The technique uses good partitioning strategies and a subspace decomposition based preconditioned iterative solver, Two level orthogonalization is used to obtain a reduced system which is preconditioned by a coarse grid operator. Numerical results show fast cOIl\'ergence for the ...

Fast-multipole and precorrected-FFT accelerated iterative methods have substantially improved the eeciency of Method-of-Moments (MOM) based 3-D electromagnetic analysis programs. In this paper we present a novel second-kind integral formulation and discretization approach for electrostatic analysis, as well as a projection technique for electroquasistatic analysis. We show that when these new a...

This paper deals with the estimation of the distance between the solution of a static linear mechanic problem and its approximation by the finite element method solved with a non-overlapping domain decomposition method (FETI or BDD). We propose a new strict upper bound of the error which separates the contribution of the iterative solver and the contribution of the discretization. Numerical ass...

This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element (FE) and domain decomposition (DD) methods. In addition to a fully parallel computation, the proposed lower bounds separate the algebraic error (due to the use of a DD iterative solver) from the discretization error (due to the FE), which enables the steering of the iterative solve...

3 Proposed Techniques – An Overview 4 3.1 Matrix Reductions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1.1 Global Threshold Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1.2 Local Threshold Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1.3 Michaelis-Menten Reduction . . . . . . . . . . . . . . . . . . . . . . . ....

In the edge vector finite element solution of the frequency domain Maxwell equations, the presence of a large kernel of the discrete rotor operator is known to ruin convergence of standard iterative solvers. We extend the approach of [1] and, using domain decomposition ideas, construct a multilevel iterative solver where the projection with respect to the kernel is combined with the use of a hi...

This report describes the design and implementation of the parallel iterative linear system solver PAISS (Parallel Adaptive Iterative linear System Solver) for distributed memory multicomputers and workstation clusters. It is capable to apply a heterogeneous data distribution and dynamic load balancing within an iterative solver routine at matrix level. Sparse and dense matrices, as well as vec...

In hardware-aware high performance computing, blockasynchronous iteration and mixed precision iterative refinement are two techniques that are applied to leverage the computing power of SIMD accelerators like GPUs. Although they use a very different approach for this purpose, they share the basic idea of compensating the convergence behaviour of an inferior numerical algorithm by a more efficie...