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FPGAbased multigrid computations for molecular dynamics simulations
 In Proceedings of the IEEE Symposium on Field Programmable Custom Computing Machines (2007
"... Abstract: FPGAbased acceleration of molecular dynamics (MD) has been the subject of several recent studies. Implementing longrange forces, however, has only recently been addressed. Here we describe a solution based on the multigrid method. We show that multigrid is, in general, an excellent ma ..."
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Abstract: FPGAbased acceleration of molecular dynamics (MD) has been the subject of several recent studies. Implementing longrange forces, however, has only recently been addressed. Here we describe a solution based on the multigrid method. We show that multigrid is, in general, an excellent match to FPGAs: the primary operations take advantage of the large number of independently addressable RAMs and the efficiency with which complex systolic structures can be implemented. The multigrid accelerator has been integrated into our existing MD system, and an overall performance gain of 5x to 7x has been obtained, depending on hardware configuration and reference code. The simulation accuracy is comparable to the original double precision serial code. 1.
COLLOCATION COARSE APPROXIMATION (CCA) IN MULTIGRID
"... Abstract. The two common approaches to defining coarse operators in multigrid numerical algorithms are discretization coarse approximation (DCA) and (Petrov)Galerkin coarse approximation (GCA). Here, a new approach called collocation coarse approximation (CCA) is introduced, which—like GCA—is algeb ..."
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Abstract. The two common approaches to defining coarse operators in multigrid numerical algorithms are discretization coarse approximation (DCA) and (Petrov)Galerkin coarse approximation (GCA). Here, a new approach called collocation coarse approximation (CCA) is introduced, which—like GCA—is algebraically defined and able to cater to difficult features such as discontinuous coefficients, but, unlike GCA, allows explicit control over the coarsegrid sparsity pattern (stencil) and therefore control over the computational complexity of the solver. CCA relies on certain basis functions for which the coarse approximation to the finegrid problem is exact. Numerical experiments for twodimensional diffusion problems including jumping coefficients demonstrate the potential of the resulting multigrid algorithms.
GOALORIENTED ADAPTIVITY AND MULTILEVEL PRECONDITIONING FOR THE POISSONBOLTZMANN EQUATION
, 1109
"... ABSTRACT. In this article, we develop goaloriented error indicators to drive adaptive refinement algorithms for the PoissonBoltzmann equation. Empirical results for the solvation free energy linear functional demonstrate that goaloriented indicators are not sufficient on their own to lead to a su ..."
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ABSTRACT. In this article, we develop goaloriented error indicators to drive adaptive refinement algorithms for the PoissonBoltzmann equation. Empirical results for the solvation free energy linear functional demonstrate that goaloriented indicators are not sufficient on their own to lead to a superior refinement algorithm. To remedy this, we propose a problemspecific marking strategy using the solvation free energy computed from the solution of the linear regularized PoissonBoltzmann equation. The convergence of the solvation free energy using this marking strategy, combined with goaloriented refinement, compares favorably to adaptive methods using an energybased error indicator. Due to the use of adaptive mesh refinement, it is critical to use multilevel preconditioning in order to maintain optimal computational complexity. We use variants of the classical multigrid method, which can be viewed as generalizations of the hierarchical basis
Discontinuous Galerkin Methods: Linear Systems and Hidden AccuracyDiscontinuous Galerkin Methods: Linear Systems and Hidden Accuracy
"... ter verkrijging van de graad van doctor ..."
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1 Introduction Amenability of Multigrid Computations to FPGABased Acceleration ∗
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First Reader
, 2008
"... While molecular dynamics simulations (MD) are a fundamental method for gaining the understanding of chemical and biological systems, their computational cost is extremely high: Simulating macromolecules requires thousands of node hours and celllevel systems remain altogether out of reach. We addres ..."
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While molecular dynamics simulations (MD) are a fundamental method for gaining the understanding of chemical and biological systems, their computational cost is extremely high: Simulating macromolecules requires thousands of node hours and celllevel systems remain altogether out of reach. We address this issue by using an emerging mode of high performance computing that is based on configurable logic in the form of Field Programmable Gate Arrays (FPGAs). The problem is that, while FPGAs have often delivered 100fold speedups per node over microprocessorbased systems, the applications have generally been limited to those with small regular kernels operating on lowprecision integer data types. MD possesses neither. We address this problem by creating an explicitly designed FPGAcoprocessor that can be integrated into generic commercially available systems. MD is an iterative technique: the forces on each particle are computed, then applied using the equations of motion. We use standard partitioning by computing bonded forces, motion updates, and bookkeeping on the host, while computing the remaining forces (which
Multilevel algorithms for combinatorial optimization problems Published papers format Advisors
"... The Multiscale method is a class of algorithmic techniques for solving efficiently and effectively largescale computational and optimization problems. This method was originally invented for solving elliptic partial differential equations and up to now it represents the most effective class of nume ..."
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The Multiscale method is a class of algorithmic techniques for solving efficiently and effectively largescale computational and optimization problems. This method was originally invented for solving elliptic partial differential equations and up to now it represents the most effective class of numerical algorithms for them. During the last two decades, there were many successful attempts to adapt the multiscale method for combinatorial optimization problems. Whereas the variety of continuous systems’ multiscale algorithms turned into a separate field of applied mathematics, for combinatorial optimization problems they still have not reached an advanced stage of development, consisting in practice of a very limited number of multiscale techniques. The main goal of this dissertation is to extend the knowledge of multiscale techniques for the combinatorial optimization problems. In the first part of this dissertation we formulate the principles of designing the multilevel algorithms for combinatorial optimization problems defined on a simple graph (or matrix) model. We present the results for a variety of linear ordering
Problem area
, 2007
"... methods are used to analyse the radar signature of military platforms when the radar signature can not be determined experimentally because: • The platform is in the design, development or procurement phase. • The platform belongs to a hostile party. For jet powered fighter aircraft, the radar signa ..."
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methods are used to analyse the radar signature of military platforms when the radar signature can not be determined experimentally because: • The platform is in the design, development or procurement phase. • The platform belongs to a hostile party. For jet powered fighter aircraft, the radar signature is dominated by the contribution of the jet engine air intake for a large range of forward observation angles. The intake can be regarded as a oneside open large and deep forward facing cavity. Although the contribution of the outer mould shape of the platform can be efficiently and accurately computed using simple scattering models, these can not be used to accurately compute the contribution of the jet engine air intake. Previously, an algorithm was developed to enable socalled full wave analysis of cavity scattering, but the computational work involved prohibits the application for analysis of jet engine air intakes at the relevant excitation frequency band. Description of work A thorough analysis of the mathematical model of full wave cavity scattering has been made. The key elements of the numerical method Report no.
U.S.A. 2Department of Geology and Geophysics and
"... The governing equations for mantle convection are derived from conservation laws of mass, momentum and energy. The nonlinear nature of mantle rheology with its strong temperature and stressdependence and nonlinear coupling between flow velocity and temperature in the energy equation require that n ..."
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The governing equations for mantle convection are derived from conservation laws of mass, momentum and energy. The nonlinear nature of mantle rheology with its strong temperature and stressdependence and nonlinear coupling between flow velocity and temperature in the energy equation require that numerical methods be used to solve these