Results 11  20
of
35
MinMaxBoundary Domain Decomposition
 Theor. Comput. Sci
, 1998
"... Domain decomposition is one of the most effective and popular parallel computing techniques for solving large scale numerical systems. In the special case when the amount of computation in a subdomain is proportional to the volume of the subdomain, domain decomposition amounts to minimizing the surf ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
(Show Context)
Domain decomposition is one of the most effective and popular parallel computing techniques for solving large scale numerical systems. In the special case when the amount of computation in a subdomain is proportional to the volume of the subdomain, domain decomposition amounts to minimizing the surface area of each subdomain while dividing the volume evenly. Motivated by this fact, we study the following minmax boundary multiway partitioning problem: Given a graph G and an integer k ? 1, we would like to divide G into k subgraphs G 1 ; : : : ; G k (by removing edges) such that (i) jG i j = \Theta(jGj=k) for all i 2 f1; : : : ; kg; and (ii) the maximum boundary size of any subgraph (the set of edges connecting it with other subgraphs) is minimized. We provide an algorithm that given G, a wellshaped mesh in d dimensions, finds a partition of G into k subgraphs G 1 ; : : : ; G k , such that for all i, G i has \Theta(jGj=k) vertices and the number of edges connecting G i with the ot...
Definition of a New Circular SpaceFilling Curve  βΩIndexing
"... This technical report presents the definition of a circular Hilbertlike spacefilling curve. Preliminary evaluations in a simulation environment have shown good locality preserving properties. The results are compared with known bounds for other indexing schemes: Hilbert, Lebesgue, and HInde ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
This technical report presents the definition of a circular Hilbertlike spacefilling curve. Preliminary evaluations in a simulation environment have shown good locality preserving properties. The results are compared with known bounds for other indexing schemes: Hilbert, Lebesgue, and HIndexing. We evaluated partitions induced by the indexing schemes and uses the diameter and the surface as measures. For both we present worst case and average case results.
Mathematical and Numerical Aspects of the Adaptive Fast Multipole PoissonBoltzmann Solver
"... Abstract. This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole PoissonBoltzmann (AFMPB) solver. We introduce and discuss the following components in order: the PoissonBoltzmann model, boundary integral equation reformulation, surfa ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
Abstract. This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole PoissonBoltzmann (AFMPB) solver. We introduce and discuss the following components in order: the PoissonBoltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to largescale longtime molecular dynamics simulations. The potential of the solver is demonstrated with preliminary numerical results.
Parallel Software for Inductance Extraction
"... The next generation VLSI circuits will be designed with millions of densely packed interconnect segments on a single chip. Inductive effects between these segments begin to dominate signal delay as the clock frequency is increased. Modern parasitic extraction tools to estimate the onchip inductive ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
The next generation VLSI circuits will be designed with millions of densely packed interconnect segments on a single chip. Inductive effects between these segments begin to dominate signal delay as the clock frequency is increased. Modern parasitic extraction tools to estimate the onchip inductive effects with high accuracy have had limited impact due to large computational and storage requirements. This paper describes a parallel software package for inductance extraction called ParIS, which is capable of analyzing interconnect configurations involving several conductors within reasonable time. The main component of the software is a novel preconditioned iterative method that is used to solve a dense complex linear system of equations. The linear system represents the inductive coupling between filaments that are used to discretize the conductors. A variant of the Fast Multipole Method is used to compute dense matrixvector products with the coefficient matrix. ParIS uses a twotier parallel formulation that allows mixed mode parallelization using both MPI and OpenMP. An MPI process is associated with each conductor. The computation within a conductor is parallelized using OpenMP. The parallel efficiency and scalability of the software is demonstrated through experiments on the IBM p690 and Intel and AMD Linux clusters. These experiments highlight the portability and efficiency of the software on multiprocessors with shared, distributed, and distributedshared memory architectures.
Average Case Quality of Partitions Induced by the Lebesgue Indexing
, 2001
"... This paper presents the quality of partitions induced by the Lebesgue curve in average case. The surface that surrounds an arbitrary index range is compared with the optimal partition in the grid, i. e. the square. The upper bound on the surface is asymptotically 3 times the optimal size. ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
This paper presents the quality of partitions induced by the Lebesgue curve in average case. The surface that surrounds an arbitrary index range is compared with the optimal partition in the grid, i. e. the square. The upper bound on the surface is asymptotically 3 times the optimal size.
Parallel Performance of Hierarchical Multipole Algorithms for Inductance Extraction ⋆
"... Abstract. Parasitic extraction techniques are used to estimate signal delay in VLSI chips. Inductance extraction is a critical component of the parasitic extraction process in which onchip inductive effects are estimated with high accuracy. In earlier work [1], we described a parallel software pack ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract. Parasitic extraction techniques are used to estimate signal delay in VLSI chips. Inductance extraction is a critical component of the parasitic extraction process in which onchip inductive effects are estimated with high accuracy. In earlier work [1], we described a parallel software package for inductance extraction called ParIS, which uses a novel preconditioned iterative method to solve the dense, complex linear system of equations arising in these problems. The most computationally challenging task in ParIS involves computing dense matrixvector products efficiently via hierarchical multipolebased approximation techniques. This paper presents a comparative study of two such techniques: a hierarchical algorithm called Hierarchical Multipole Method (HMM) and the wellknown Fast Multipole Method (FMM). We investigate the performance of parallel MPIbased implementations of these algorithms on a Linux cluster. We analyze the impact of various algorithmic parameters and identify regimes where HMM is expected to outperform FMM on uniprocessor as well as multiprocessor platforms. 1
An Efficient and HighOrder Accurate Boundary Integral Solver for the Stokes Equations in Three Dimensional Complex Geometries
, 2004
"... ..."
(Show Context)
Communication Complexity of the Fast Multipole Method and its Algebraic Variants
"... A combination of hierarchical treelike data structures and data access patterns from fast multipole methods and hierarchical lowrank approximation of linear operators from Hmatrix methods appears to form an algorithmic path forward for efficient implementation of many linear algebraic operations ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
A combination of hierarchical treelike data structures and data access patterns from fast multipole methods and hierarchical lowrank approximation of linear operators from Hmatrix methods appears to form an algorithmic path forward for efficient implementation of many linear algebraic operations of scientific computing at the exascale. The combination provides asymptotically optimal computational and communication complexity and applicability to large classes of operators that commonly arise in scientific computing applications. A convergence of the mathematical theories of the fast multipole and Hmatrix methods has been underway for over a decade. We recap this mathematical unification and describe implementation aspects of a hybrid of these two compelling hierarchical algorithms on hierarchical distributedshared memory architectures, which are likely to be the first to reach the exascale. We present a new communication complexity estimate for fast multipole methods on such architectures. We also show how the data structures and access patterns of Hmatrices for lowrank operators map onto those of fast multipole, leading to an algebraically generalized form of fast multipole that compromises none of its architecturally ideal properties.