In this paper, a comparison of parallel beam-tracing methods is presented and an original parallel domain decomposition method is proposed to solve numerical acoustic problems. A hybrid method between the ray-tracing and the beam-tracing method is first introduced. Then, classical parallelization methods are exposed and compared on shared and distributed memory architectures. Finally, a new parallel method based on domain decomposition principles is proposed. This method allows to handling large-scale problems better than other existing methods when taking into account the input/output and preprocessing steps. Parallel numerical experiments, carried out on a real world problem -namely the acoustic pollution analysis within a large city-illustrate the performance of this new domain decomposition method.
In this paper, a new coarse space based on Chebyshev polynomials is considered as a preconditioning technique for the solution of algebraic systems of equations arising from image reconstruction. These systems are commonly obtained from the use of Compactly-Supported Radial Basis Functions for interpolating scattered image data. Here an efficient and robust coarse space preconditioning technique is presented and the convergence behaviour of the associated iterative method upon different types of functions used for designing the coarse space is studied.
Engineering problems involve the solution of large sparse linear systems, and require therefore fast and high performance algorithms for algebra operations such as dot product, and matrix-vector multiplication. During the last decade, graphics processing units have been widely used. In this paper, linear algebra operations on graphics processing unit for single and double precision (with real and complex arithmetic) are analyzed in order to make iterative Krylov algorithms efficient compared to central processing units implementation. The performance of the proposed method is evaluated for the Laplace and the Helmholtz equations. Numerical experiments clearly show the robustness and effectiveness of the graphics processing unit tuned algorithms for compressed-sparse row data storage.