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27
The Adaptive Multilevel Finite Element Solution of the PoissonBoltzmann Equation on Massively Parallel Computers
 J. COMPUT. CHEM
, 2000
"... Using new methods for the parallel solution of elliptic partial differential equations, the teraflops computing power of massively parallel computers can be leveraged to perform electrostatic calculations on large biological systems. This paper describes the adaptive multilevel finite element soluti ..."
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Cited by 43 (14 self)
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Using new methods for the parallel solution of elliptic partial differential equations, the teraflops computing power of massively parallel computers can be leveraged to perform electrostatic calculations on large biological systems. This paper describes the adaptive multilevel finite element solution of the PoissonBoltzmann equation for a microtubule on the NPACI IBM Blue Horizon supercomputer. The microtubule system is 40 nm in length and 24 nm in diameter, consists of roughly 600,000 atoms, and has a net charge of1800 e. PoissonBoltzmann calculations are performed for several processor configurations and the algorithm shows excellent parallel scaling.
Local and parallel finite element algorithms based on twogrid discretizations
 Math. Comput
"... Abstract. A number of new local and parallel discretization and adaptive finite element algorithms are proposed and analyzed in this paper for elliptic boundary value problems. These algorithms are motivated by the observation that, for a solution to some elliptic problems, low frequency components ..."
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Cited by 18 (4 self)
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Abstract. A number of new local and parallel discretization and adaptive finite element algorithms are proposed and analyzed in this paper for elliptic boundary value problems. These algorithms are motivated by the observation that, for a solution to some elliptic problems, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure. The theoretical tools for analyzing these methods are some local a priori and a posteriori estimates that are also obtained in this paper for finite element solutions on general shaperegular grids. Some numerical experiments are also presented to support the theory. 1.
A New Parallel Domain Decomposition Method for the Adaptive Finite Element Solution of Elliptic Partial Differential Equations
, 1999
"... We present a new domain decomposition algorithm for the parallel finite element solution of elliptic partial differential equations. As with most parallel domain decomposition methods each processor is assigned one or more subdomains and an iteration is devised which allows the processors to solv ..."
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Cited by 12 (10 self)
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We present a new domain decomposition algorithm for the parallel finite element solution of elliptic partial differential equations. As with most parallel domain decomposition methods each processor is assigned one or more subdomains and an iteration is devised which allows the processors to solve their own subproblem(s) concurrently. The novel feature of this algorithm however is that each of these subproblems is defined over the entire domain  although the vast majority of the degrees of freedom for each subproblem are associated with a single subdomain (owned by the corresponding processor). This ensures that a global mechanism is contained within each of the subproblems tackled and so no separate coarse grid solve is required in order to achieve rapid convergence of the overall iteration. Furthermore, by following the paradigm introduced in [5], it is demonstrated that this domain decomposition solver may be coupled easily with a conventional mesh refinement code, thus...
Parallel geometric multigrid
 Numerical Solution of Partial Differential Equations on Parallel Computers, volume 51 of LNCSE, chapter 5
, 2005
"... Summary. Multigrid methods are among the fastest numerical algorithms for the solution of large sparse systems of linear equations. While these algorithms exhibit asymptotically optimal computational complexity, their efficient parallelisation is hampered by the poor computationtocommunication rat ..."
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Cited by 9 (6 self)
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Summary. Multigrid methods are among the fastest numerical algorithms for the solution of large sparse systems of linear equations. While these algorithms exhibit asymptotically optimal computational complexity, their efficient parallelisation is hampered by the poor computationtocommunication ratio on the coarse grids. Our contribution discusses parallelisation techniques for geometric multigrid methods. It covers both theoretical approaches as well as practical implementation issues that may guide code development. 1
FeaturePreserving Adaptive Mesh Generation for Molecular Shape Modeling and Simulation
, 2007
"... We describe a chain of algorithms for molecular surface and volumetric mesh generation. We take as inputs the centers and radii of all atoms of a molecule and the toolchain outputs both triangular and tetrahedral meshes that can be used for molecular shape modeling and simulation. Experiments on a n ..."
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Cited by 8 (5 self)
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We describe a chain of algorithms for molecular surface and volumetric mesh generation. We take as inputs the centers and radii of all atoms of a molecule and the toolchain outputs both triangular and tetrahedral meshes that can be used for molecular shape modeling and simulation. Experiments on a number of molecules are demonstrated, showing that our methods possess several desirable properties: featurepreservation, local adaptivity, high quality, and smoothness (for surface meshes). We also demonstrate an example of molecular simulation using the finite element method and the meshes generated by our method. The approaches presented and their implementations are also applicable to other types of inputs such as 3D scalar volumes and triangular surface meshes with low quality, and hence can be used for generation/improvment of meshes in a broad range of applications.
Parallel performance prediction for numerical codes in a multicluster environment
 In Proc. of the 2008 International Multiconference on Comp. Science and Information Technology (IMCSIT’08
, 2008
"... Abstract—We propose a model for describing and predicting the performance of parallel numerical software on distributed memory architectures within a multicluster environment. The goal of the model is to allow reliable predictions to be made as to the execution time of a given code on a large numbe ..."
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Cited by 6 (2 self)
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Abstract—We propose a model for describing and predicting the performance of parallel numerical software on distributed memory architectures within a multicluster environment. The goal of the model is to allow reliable predictions to be made as to the execution time of a given code on a large number of processors of a given parallel system, and on a combination of systems, by only benchmarking the code on small numbers of processors. This has potential applications for the scheduling of jobs in a Grid computing environment where informed decisions about which resources to use in order to maximize the performance and/or minimize the cost of a job will be valuable. The methodology is built and tested for a particular class of numerical code, based upon the multilevel solution of discretized partial differential equations, and despite its simplicity it is demonstrated to be extremely accurate and robust with respect to both the processor and communications architectures considered. Furthermore, results are also presented which demonstrate that excellent predictions may also be obtained for numerical algorithms that are more general than the pure multigrid solver used to motivate the methodology. These are based upon the use of a practical parallel engineering code that is briefly described. The potential significance of this work is illustrated via two scenarios which consider a Grid user who wishes to use the available resources either (i) to obtain a particular result as quickly as possible, or (ii) to obtain results to different levels of accuracy.
HighFidelity Geometric Modeling for Biomedical Applications
"... We describe a combination of algorithms for high fidelity geometric modeling and mesh generation. Although our methods and implementations are applicationneutral, our primary target application is multiscale biomedical models that range in scales across the molecular, cellular, and organ levels. Ou ..."
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Cited by 6 (4 self)
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We describe a combination of algorithms for high fidelity geometric modeling and mesh generation. Although our methods and implementations are applicationneutral, our primary target application is multiscale biomedical models that range in scales across the molecular, cellular, and organ levels. Our software toolchain implementing these algorithms is general in the sense that it can take as input a molecule in PDB/PQR forms, a 3D scalar volume, or a userdefined triangular surface mesh that may have very low quality. The main goal of our work presented is to generate high quality and smooth surface triangulations from the aforementioned inputs, and to reduce the mesh sizes by mesh coarsening. Tetrahedral meshes are also generated for finite element analysis in biomedical applications. Experiments on a number of biostructures are demonstrated, showing that our approach possesses several desirable properties: featurepreservation, local adaptivity, high quality, and smoothness (for surface meshes). The availability of this software toolchain will give researchers in computational biomedicine and other modeling areas access to higherfidelity geometric models.
Partitioning and Dynamic Load Balancing for the Numerical Solution of Partial Differential Equations
 Numerical Solution of Partial Differential Equations on Parallel Computers
, 2005
"... lement methods, have workloads that are unpredictable or change during the computation, requiring dynamic load balancers that adjust the decomposition as the computation proceeds. Partitioning approaches attempt to distribute computational work equally, while minimizing interprocessor communication ..."
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Cited by 5 (1 self)
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lement methods, have workloads that are unpredictable or change during the computation, requiring dynamic load balancers that adjust the decomposition as the computation proceeds. Partitioning approaches attempt to distribute computational work equally, while minimizing interprocessor communication costs. Communication costs are governed by the amount of data to be shared by cooperating processes (communication volume) and the number of partitions sharing the data (number of messages). Dynamic loadbalancing procedures should also operate in parallel on distributed data, execute quickly, and minimize data movement by making the new data distribution as similar as possible to the existing one. The partitioning problem is defined in more detail in Section 1. Numerous partitioning strategies have been developed. The various strategies are distinguished by tradeo#s between partition quality, amount of data movement, and partitioning speed. Characteristics of an application (e.g., computat
A domain decomposition solver for a parallel adaptive meshing paradigm
 SIAM J. SCI. COMPUT
"... We describe a domain decomposition algorithm for use in the parallel adaptive meshing paradigm of Bank and Holst. Our algorithm has low communication, makes extensive use of existing sequential solvers, and exploits in several important ways data generated as part of the adaptive meshing paradigm. ..."
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Cited by 4 (1 self)
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We describe a domain decomposition algorithm for use in the parallel adaptive meshing paradigm of Bank and Holst. Our algorithm has low communication, makes extensive use of existing sequential solvers, and exploits in several important ways data generated as part of the adaptive meshing paradigm. Numerical examples illustrate the effectiveness of the procedure.
Parallel Application of a Novel Domain Decomposition Preconditioner for the Adaptive Finite Element Solution of ThreeDimensional ConvectionDominated PDEs
, 2001
"... this paper we provide details of our 3d parallel implementation and demonstrate that the technique may be generalized to the solution of nonsymmetric algebraic systems, such as those arising when convectiondiusion problems are discretized using either Galerkin or stabilized nite element methods ..."
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Cited by 3 (2 self)
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this paper we provide details of our 3d parallel implementation and demonstrate that the technique may be generalized to the solution of nonsymmetric algebraic systems, such as those arising when convectiondiusion problems are discretized using either Galerkin or stabilized nite element methods (FEMs). Furthermore we illustrate the potential of the preconditioner for use within an adaptive nite element framework by successfully solving convectiondominated problems on locally, rather than globally, re ned meshes. key words: Domain decomposition; additive Schwarz; weakly overlapping; convectiondiusion