Communication costs have become a performance bottleneck in many applications, and are a big issue for high performance computing on massively parallel machines. This paper proposes a halo exchange method for unstructured sparse matrix vector products within the algebraic multigrid method, and evaluate it on a supercomputer with mesh/torus networks. In our numerical tests with a Poisson problem, the proposed method accelerates the linear solver more than 14 times with 23040 cores.

The bilateral filter (BF) is a nonlinear and low-pass filter which can smooth an image while preserving detail structures. However, the filer is time consuming for real-time processing. In this paper, we bring forward a fresh idea that bilateral filtering can be accelerated by a multigrid (MG) scheme. Our method is based on the following two facts. a) The filtering result by a BF with a large kernel size on the original resolution can be approximated by applying a small kernel sized (3×3) version on the lower resolution many times on the premise of visual acceptance. Early work has shown that a BF can be viewed as nonlinear diffusion. The desired filtering result is actually an intermediate status of the diffusion process. b) Iterative linear equation techniques are sufficiently mature to cope with the nonlinear diffusion equation, which can be accelerated by the MG scheme. Experimental results with both simulated data sets and real sets are provided, and the new method is demonstrated to achieve almost twice the speed of the state-of-the-art. Compared with previous efforts for finding a generalized representation to link bilateral filtering and nonlinear diffusion by adaptive filtering, a novel relationship between nonlinear diffusion and bilateral filtering is explored in this study by focusing attention on numerical calculus.

An iterative reconstruction algorithm of accelerating the estimation of the complex relative permittivity of a cylindrical dielectric object based on the multigrid optimization method (MGOM) is presented. A cost functional is defined by the norm of a difference between the scattered electric fields measured and calculated for an estimated contrast function, which is expressed as a function of the complex relative permittivity of the object. Then the electromagnetic inverse scattering problem can be treated as an optimization problem where the contrast function is determined by minimizing the cost functional. We apply the conjugate gradient method (CGM) and the frequency-hopping technique (FHT) to the minimization of the cost functional, and also employ the multigrid method (MGM) with a V-cycle to accelerate the rate of convergence for getting the reconstructed profile. The reconstruction scheme is called the multigrid optimization method. Computer simulations are performed for lossy and inhomogeneous dielectric circular cylinders by using single-frequency or multifrequency scattering data. The numerical results demonstrate that the rate of convergence of the proposed metod is much faster than that of the conventional CGM for both noise-free and noisy cases.

Scattering of a Gaussian beam by dielectric cylinders with arbitrary shape is analyzed by using the moment method combined with multigrid method. The effectiveness of the multigrid-moment method is firstly shown from the CPU time and residual norm viewpoints. The effect of the initial value for the multigrid cycle is also considered. After that, the scattered fields by two dielectric convex lens are calculated and the effect of the radius of curvature, width and the distance between each lens on the scattered field is examined.

The purpose of this paper is to discuss length estimation based on digitized curves. Information on a curve in the Euclidean plane is lost after digitization. Higher resolution supports a convergence of a digital image towards the original curve with respect to Hausdorff metric. No matter how high resolution is assumed, it is impossible to know the length of an original curve exactly. In image analysis we estimate the length of a curve in the Euclidean plane based on an approximation. An approximate polygon converges to the original curve with an increase of resolution. Several approximation methods have been proposed so far. This paper proposes a new approximation method which generates polygonal curves closer (in the sense of Hausdorff metric) in general to its original curves than any of the previously known methods and discusses its relevance for length estimation by proving a Convergence Theorem.

The performance of a drift-diffusion device simulator using massively parallel processors is improved by modifying the preconditioner for the iterative solver and by improving the initial guess for the Newton loop. A grid-to-processor mapping scheme is presented to implement the partitioned natural ordering preconditioner on the CM-5. A new preconditioner called the block partitioned natural ordering, which may include fill-ins, improves performance in terms of CPU time and convergence behavior on the CM-5. A multigrid discretization to implement a block Newton initial guess routine is observed to decrease the CPU time by a factor of two. Extensions of the initial guess routine show further reduction in the final fine grid linear iterations.

In this letter, we propose an algorithm to estimate the optical flow fields based on a hierarchical structure composed of spatio-temporal image pyramids obtained from repetitive application of the Gaussian filtering and decimation in both the spatial and temporal domain. In our approach, an inter-level motion smoothness constraint between adjacent pyramid levels is introduced to estimate a unique optical flow field. We show that the pyramid structure allows us to employ the multigrid algorithm, which is known to accelerate the convergence rate. The multigrid algorithm provides a scheme for efficient combination of local and global information to estimate the optical flow field. The experimental results reveal that the combination of local and global information yields a fast convergence behavior and accurate motion estimation results.