On the Convergence Behavior of IDR(s) and Related Methods

An explanation is given of the convergence behavior of IDR(s) methods. The convergence mechanism of these algorithms has two components. The first consists of damping properties of certain factors in the residual polynomials, which becomes less important for large values of s. The second component depends on the behavior of Lanczos polynomials...

The Deflated Preconditioned Conjugate Gradient Method Applied to Composite Materials

Simulations with composite materials often involve large jumps in the coefficients of the underlying stiffness matrix. These jumps can introduce unfavorable eigenvalues in the spectrum of the stiffness matrix. We show that the rigid body modes; the translations and rotations, of the disjunct rigid bodies in the composite material correspond to...

Comparison of fundamental, second harmonic, and superharmonic imaging: A simulation study

In medical ultrasound, fundamental imaging (FI) uses the reflected echoes from the same spectral band as that of the emitted pulse. The transmission frequency determines the trade-off between penetration depth and spatial resolution. Tissue harmonic imaging (THI) employs the second harmonic of the emitted frequency band to construct images....

Efficient Iterative Solution of Large Linear Systems on Heterogeneous Computing Systems

This dissertation deals mainly with the design, implementation, and analysis of efficient iterative solution methods for large sparse linear systems on distributed and heterogeneous computing systems as found in Grid computing. First, a case study is performed on iteratively solving large symmetric linear systems on both a multi–cluster and a...

Interpreting IDR(s) as a deflation method

In this paper the IDR(s) method is interpreted in the context of deflation methods. It is shown that IDR(s) can be seen as a Richardson iteration preconditioned by a variable deflation–type preconditioner. The main result of this paper is the IDR projection theorem, which relates the spectrum of the deflated system in each IDR(s) cycle to all...

Exploiting the flexibility of IDR(s) for grid computing

The IDR(s) method that is proposed in [26] is an efficient limited memory method for solving large nonsymmetric systems of linear equations. In [11] an IDR(s) variant is described that has a single synchronisation point per iteration step, which makes this variant well-suited for parallel and grid computing. In this paper, we combine this IDR(s)...

An iterative method for the computation of nonlinear, wide-angle, pulsed acoustic fields of medical diagnostic transducers

The development and optimization of medical ultrasound transducers and imaging modalities require a computational method that accurately predicts the nonlinear acoustic pressure field. A prospective method should provide the wide-angle, pulsed field emitted by an arbitrary planar source distribution and propagating in a three-dimensional, large...

A filtered convolution method for the computation of acoustic wave fields in very large spatiotemporal domains

The full-wave computation of transient acoustic fields with sizes in the order of 100x100x100 wavelengths by 100 periods requires a numerical method that is extremely efficient in terms of storage and computation. Iterative integral equation methods offer a good performance on these points, provided that the recurring spatiotemporal convolutions...

A new iterative solver for the time-harmonic wave equation

The time-harmonic wave equation, also known as the Helmholtz equation, is obtained if the constant-density acoustic wave equation is transformed from the time domain to the frequency domain. Its discretization results in a large, sparse, linear system of equations. In two dimensions, this system can be solved efficiently by a direct method. In...

Fast solution of nonsymmetric linear systems on Grid computers using parallel variants of IDR(s)

IDR(s) is a family of fast algorithms for iteratively solving large nonsymmetric linear systems [14]. With cluster computing and in particular with Grid computing, the inner product is a bottleneck operation. In this paper, three techniques are combined in order to alleviate this bottleneck. Firstly, the efficient and stable IDR(s) algorithm...