Parallel ocean flow computations on a regular and on an irregular grid

Ocean flow problems can be discretized and solved on a regular grid, by taking l and points into account in the computations, or on an irregular grid. In the latter approach, the number of unknowns is less than for the regular grid. The data structures are completely different for the two approaches. As a consequence, different nummerical techniques may be required. In this paper we study different preconditioners, based on the EBE-preconditioner that was initially proposed by Hughes et al. We also show how the algorithms can be parallelized and we give results ontained on a cluster of workstations

The parallel computation of the smallest eigenpair of an acoustic problem with damping

Acoustic problems with damping may give rise to large quadratic eigenproblems. Efficient and parallelizable algorithms are required for solving these problems. The recently proposed Jacobi-Davidson method is well suited for parallel computing: no matrix decomposition and no back or forward substitutions are needed. This paper describes the parallel solution of the smallest eigenpair of a realistic and very large quadratic eigenproblem with the Jacobi-Davidson method

The parallel computation of the smallest eigenpair of an acoustic problem with damping

Acoustic problems with damping may give rise to large quadratic eigenproblems, which require efficient and parallelizable solution algorithms. This paper describes such an algorithm: the Jacobi-Davidson solution method for quadratic eigenproblems. In particular, it describes its parallelization according to the Bulk Synchronous Programming model, and its implementation on the massively parallel CRAY T3D. Experimental results for a large-scale acoustic problem show that the method is efficient and parallelizes well, i.e. scales almost linearly up to the maximum number of available processors. Copyright © 1999 John Wiley & Sons, Ltd

Iterative solution methods for linear equations in finite element computations

Electrical Engineering, Mathematics and Computer Scienc

An efficient two-level preconditioner for multi-frequency wave propagation problems

We consider wave propagation problems that are modeled in the frequency-domain, and that need to be solved simultaneously for multiple frequencies within a fixed range. For this, a single shift-and-invert preconditioner at a so-called seed frequency is applied. The choice of the seed is crucial for the performance of preconditioned multi-shift GMRES and is closely related to the parameter choice for the Complex Shifted Laplace preconditioner. Based on a classical GMRES convergence bound, we present an analytic formula for the optimal seed parameter that purely depends on the original frequency range. The new insight is exploited in a two-level preconditioning strategy: A shifted Neumann preconditioner with minimized spectral radius is additionally applied to multi-shift GMRES. Moreover, we present a reformulation of the multi-shift problem to a matrix equation solved with, for instance, global GMRES. Here, our analysis allows for rotation of the spectrum of the linear operator. Numerical experiments for the time-harmonic visco-elastic wave equation demonstrate the performance of the new preconditioners.</p

Shallow-water acoustic communication with high bit rate BPSK signals

BPSK signals have been defined for transmission through a shallow-water acoustic communication channel. The signals were accompanied by two displaced carriers to facilitate carrier recovery. To correct for the adverse effects of time spreading, a pseudo-random learning sequence was transmitted ahead of the communication signal. The signal processing consists of a shift to baseband guided by the displaced carriers, a least-squares equalizer tuned to the received learning signal, coherent addition of reconstructed baseband signals (corresponding to selected channels of the receiving hydrophone array), and bit restoration with a decision-directed equalizer. In this manner, bit rates up to 4 kbit/s are successfully dealt with in moving-point-to-fixed-point communication. The main risk appears to be the fading of a displaced carrier

An elegant IDR(s) variant that efficiently exploits bi-orthogonality properties

Electrical Engineering, Mathematics and Computer Scienc

An efficient two-level preconditioner for multi-frequency wave propagation problems

We consider wave propagation problems that are modeled in the frequency-domain, and that need to be solved simultaneously for multiple frequencies within a fixed range. For this, a single shift-and-invert preconditioner at a so-called seed frequency is applied. The choice of the seed is crucial for the performance of preconditioned multi-shift GMRES and is closely related to the parameter choice for the Complex Shifted Laplace preconditioner. Based on a classical GMRES convergence bound, we present an analytic formula for the optimal seed parameter that purely depends on the original frequency range. The new insight is exploited in a two-level preconditioning strategy: A shifted Neumann preconditioner with minimized spectral radius is additionally applied to multi-shift GMRES. Moreover, we present a reformulation of the multi-shift problem to a matrix equation solved with, for instance, global GMRES. Here, our analysis allows for rotation of the spectrum of the linear operator. Numerical experiments for the time-harmonic visco-elastic wave equation demonstrate the performance of the new preconditioners.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Numerical Analysi

Parallel scientific computing on loosely coupled networks of computers

Electrical Engineering, Mathematics and Computer Scienc

Implementing the conjugate gradient method on a grid computer

Electrical Engineering, Mathematics and Computer Scienc