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218
Efficient Numerical Shadowing Global Error Estimation for High Dimensional Dissipative Systems∗
, 2004
"... Shadowing is a means of characterizing global errors in the numerical solution of initial value differential equations by allowing for small perturbations in the initial conditions. The method presented in this paper provides a technique for efficient estimation of the shadowing global error for sys ..."
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Shadowing is a means of characterizing global errors in the numerical solution of initial value differential equations by allowing for small perturbations in the initial conditions. The method presented in this paper provides a technique for efficient estimation of the shadowing global error
Multidomain Local Fourier Method for PDEs in Complex Geometries
, 1996
"... A low communication parallel algorithm is developed for the solution of timedependent nonlinear PDEs. The parallelization is achieved by domain decomposition. The discretization in time is performed via a third order semiimplicit stiffly stable scheme. The elemental solutions in the subdomains are ..."
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Cited by 5 (3 self)
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A low communication parallel algorithm is developed for the solution of timedependent nonlinear PDEs. The parallelization is achieved by domain decomposition. The discretization in time is performed via a third order semiimplicit stiffly stable scheme. The elemental solutions in the subdomains
Adaptivesparse polynomial dimensional decomposition for highdimensional stochastic computing
 Comput. Methods Appl. Math
"... a b s t r a c t This article presents two novel adaptivesparse polynomial dimensional decomposition (PDD) methods for solving highdimensional uncertainty quantification problems in computational science and engineering. The methods entail global sensitivity analysis for retaining important PDD co ..."
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Cited by 2 (1 self)
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a b s t r a c t This article presents two novel adaptivesparse polynomial dimensional decomposition (PDD) methods for solving highdimensional uncertainty quantification problems in computational science and engineering. The methods entail global sensitivity analysis for retaining important PDD
Global Communication Schemes on QCDOC 1 2
"... We present a global Allgather communication algorithm on the QCDOC, a switchless architecture with nearest neighbor communications on a high dimensional torus. This communication is needed for several applications, such as the molecular dynamics algorithm involving Ewald summation for longranged in ..."
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We present a global Allgather communication algorithm on the QCDOC, a switchless architecture with nearest neighbor communications on a high dimensional torus. This communication is needed for several applications, such as the molecular dynamics algorithm involving Ewald summation for long
High order schemes based on operator splitting and deferred corrections for stiff time dependent PDE’s
, 2014
"... We consider quadrature formulas of high order in time based on Radau–type, L–stable implicit Runge–Kutta schemes to solve time dependent stiff PDEs. Instead of solving a large nonlinear system of equations, we develop a method that performs iterative deferred corrections to compute the solution at t ..."
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We consider quadrature formulas of high order in time based on Radau–type, L–stable implicit Runge–Kutta schemes to solve time dependent stiff PDEs. Instead of solving a large nonlinear system of equations, we develop a method that performs iterative deferred corrections to compute the solution
A HighOrder Global Spatially Adaptive Collocation Method for 1D Parabolic PDEs
"... In this paper, we describe a highorder solver, adaptive in space and time, for the efficient numerical solution of onedimensional parabolic PDEs. Collocation at Gaussian points is employed for the spatial discretization, using a Bspline basis. A modification of the well known DAE solver, DASSL i ..."
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Cited by 7 (1 self)
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In this paper, we describe a highorder solver, adaptive in space and time, for the efficient numerical solution of onedimensional parabolic PDEs. Collocation at Gaussian points is employed for the spatial discretization, using a Bspline basis. A modification of the well known DAE solver, DASSL
pp. X–XX COMPACTNESS OF DISCRETE APPROXIMATE SOLUTIONS TO PARABOLIC PDES APPLICATION TO A TURBULENCE MODEL
"... (Communicated by the associate editor name) Abstract. In this paper, we prove an adaptation of the classical compactness AubinSimon lemma to sequences of functions obtained through a sequence of discretizations of a parabolic problem. The main difficulty tackled here is to generalize the classical ..."
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proof to handle the dependency of the norms controlling each function u (n) of the sequence with respect to n. This compactness result is then used to prove the convergence of a numerical scheme combining finite volumes and finite elements for the solution of a reduced turbulence problem. 1
A High Dimensional Moving Mesh Strategy
 Appl. Numer. Math
, 1997
"... A moving mesh strategy for solving high dimensional PDEs is presented along the lines of the moving mesh PDE (MMPDE) approach recently developed in one dimension by the authors and their collaborators. With this strategy, a moving mesh PDE is formulated from the gradient flow equation for a suitable ..."
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Cited by 22 (14 self)
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A moving mesh strategy for solving high dimensional PDEs is presented along the lines of the moving mesh PDE (MMPDE) approach recently developed in one dimension by the authors and their collaborators. With this strategy, a moving mesh PDE is formulated from the gradient flow equation for a
A posteriori error estimates for nonlinear problems. Finite element discretizations of elliptic equations
 475 (1994) MR 94j:65136
"... Abstract. Using the abstract framework of [9] we analyze a residual a posteriori error estimator for spacetime finite element discretizations of quasilinear parabolic pdes. The estimator gives global upper and local lower bounds on the error of the numerical solution. The finite element discretizat ..."
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Cited by 70 (2 self)
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Abstract. Using the abstract framework of [9] we analyze a residual a posteriori error estimator for spacetime finite element discretizations of quasilinear parabolic pdes. The estimator gives global upper and local lower bounds on the error of the numerical solution. The finite element
Numerical simulation of turbulent bubbly flows
 In: Proceedings of the Third International Symposium on TwoPhase Flow Modeling and Experimentation
, 2004
"... A mathematical model for turbulent gasliquid flows with mass transfer and chemical reactions is presented and a robust solution strategy based on nested iterations is proposed for the numerical treatment of the intricately coupled PDEs. In particular, the incompressible NavierStokes equations are ..."
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Cited by 16 (7 self)
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A mathematical model for turbulent gasliquid flows with mass transfer and chemical reactions is presented and a robust solution strategy based on nested iterations is proposed for the numerical treatment of the intricately coupled PDEs. In particular, the incompressible NavierStokes equations
Results 1  10
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218