FISC (Fast Illinois Solver Code), co-developed by the Center for Computational Electromagnetics, University of Illinois, and DEMACO, is designed to compute the RCS of a target described by a triangular-facet file. The...
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FISC (Fast Illinois Solver Code), co-developed by the Center for Computational Electromagnetics, University of Illinois, and DEMACO, is designed to compute the RCS of a target described by a triangular-facet file. The problem is formulated using the Method of Moments (MoM), where the Rao, Wilton, and Glisson basis functions are used. The resultant matrix equation is solved iteratively by the Conjugate Gradient (CG) method. The multilevel Fast Multipole algorithm (MLFMA) is used to speed up the matrix-vector multiply in the CG method. The complexities for both the CPU time per iteration and the memory requirements are of O(N log N), where N is the number of unknowns. A 2.4-million unknown problem is solved in a few hours on the SGI GRAY Origin 2000 at NCSA of the University of Illinois at Urbana-Champaign.
We study if the multilevel algorithm introduced in Debussche et al. (Theor: Comput. Fluid Dynam., 7, 279-315 (1995)) and Dubois et al. (J. Sci. Comp., 8, 167-194 (1993)) for the 2D Navier-Stokes equations with periodi...
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We study if the multilevel algorithm introduced in Debussche et al. (Theor: Comput. Fluid Dynam., 7, 279-315 (1995)) and Dubois et al. (J. Sci. Comp., 8, 167-194 (1993)) for the 2D Navier-Stokes equations with periodic boundary conditions and spectral discretization can be generalized to more general boundary conditions and to finite elements. We first show that a direct generalization, as in Calgaro et al. (Appl. Numer. Math., 21, 1-40 (1997)), for the Burgers equation, would not be very efficient. We then propose a new approach where the domain of integration is decomposed in subdomains. This enables us to define localized small-scale components and we show that, in this context, there is a good separation of scales. We conclude that all the ingredients necessary for the implementation of the multilevel algorithm are present. (C) 1998 John Wiley & Sons, Ltd.
An accurate and efficient technique called the thin-stratified medium fast-multipole algorithm (TSM-FMA) is presented for solving integral equations pertinent to electromagnetic analysis of microstrip structures, whic...
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An accurate and efficient technique called the thin-stratified medium fast-multipole algorithm (TSM-FMA) is presented for solving integral equations pertinent to electromagnetic analysis of microstrip structures, which consists of the full-wave analysis method and the application of the multilevel fast multipole algorithm (MLFMA) to thin stratified structures, In this approach, a new form of the electric-field spatial-domain Green's function is developed in a symmetrical form which simplifies the discretization of the integral equation using the method of moments (MoM). The patch mag be of arbitrary shape since their equivalent electric currents are modeled with subdomain triangular patch basis functions, TSM-FMA is introduced to speed up the matrix-vector multiplication which constitutes the major computational cost in the application of the conjugate gradient (CG) method, TSM-FMA reduces the central processing unit (CPU) time per iteration to O(N log N) for sparse structures and to O(N) for dense structures, from O(N-3) for the Gaussian elimination method and O(N-3) per iteration for the CG method, The memory requirement for TSM-FMA also scales as O(N log N) for sparse structures and as O(N) for dense structures, Therefore, this approach is suitable for solving large-scale problems on a small computer.
In the solution of an integral equation using the conjugate gradient (CG) method, the most expensive part is the matrix-vector multiplication, requiring O(N2) floating-point operations. The fast multipole method (FMM)...
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In the solution of an integral equation using the conjugate gradient (CG) method, the most expensive part is the matrix-vector multiplication, requiring O(N2) floating-point operations. The fast multipole method (FMM) reduced the operation to O(N1-5). In this article we apply a multilevel algorithm to this problem and show that the complexity of a matrix-vector multiplication is proportional to N (log(N))2. (C) 1994 John Wiley & Sons, Inc.
The fast multipole method (FMM) has been implemented to speed up the matrix-vector multiply when an iterative method is used to solve the combined field integral equation (CFIE). FMM reduces the complexity from O(N-2)...
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The fast multipole method (FMM) has been implemented to speed up the matrix-vector multiply when an iterative method is used to solve the combined field integral equation (CFIE). FMM reduces the complexity from O(N-2) to O(N-1.5). With a multilevel fast multipole algorithm (MLFMA), it is further reduced to O(N log N). A 110, 592-unknown problem can be solved within 24 h on a SUN Sparc10. (C) 1995 John Wiley & Sons, Inc.
We consider the problem of dynamic load balancing for multiprocessors, for which a typical application is a parallel finite element solution method using non-structured grids and adaptive grid refinement. This type of...
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We consider the problem of dynamic load balancing for multiprocessors, for which a typical application is a parallel finite element solution method using non-structured grids and adaptive grid refinement. This type of application requires communication between the subproblems which arises from the interdependencies in the data. A load balancing algorithm should ideally not make any assumptions about the physical topology of the parallel machine. Further requirements are that the procedure should be both fast and accurate. An new multi-level algorithm is presented for solving the dynamic load balancing problem which has these properties and whose parallel complexity is logarithmic in the number of processors used in the computation.
Four totally parallel algorithms for the solution of a sparse linear system have common characteristics which become quite apparent when they are implemented on a highly parallel hypercube such as the CM2. These four ...
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Four totally parallel algorithms for the solution of a sparse linear system have common characteristics which become quite apparent when they are implemented on a highly parallel hypercube such as the CM2. These four algorithms are Parallel Superconvergent Multigrid (PSMG) of Frederickson and McBryan, Robust Multigrid (RMG) of Hackbusch, the FFT based Spectral algorithm, and Parallel Cyclic Reduction. In fact, all four can be formulated as particular cases of the same totally parallel multilevel algorithm, which we will refer to as TPMA. In certain cases the spectral radius of TPMA is zero, and it is recognized to be a direct algorithm. In many other cases the spectral radius, although not zero, is small enough that a single iteration per timestep keeps the local error within the required tolerance.
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