Diffusion models and their accelerated solution in image and surface processing.
Discontinuous Galerkin method for the simulation of 3D viscous compressible flows
EasyMSG : tools and techniques for an adaptive overlapping in SPMD programming
During the development of a parallel solver for Maxwell equations by integral formulations and Fast Multipole Method (FMM), we needed to optimize a critical part including a lot of communications and computations. Generally, many parallel programs need to communicate, but choosing explicitly the way and the instant may decrease the efficiency of the overall program. So, the overlapping of computations and communications may be a way to reduce this drawback. We will see a implementation of this techniques...
EasyMSG: Tools and techniques for an adaptive overlapping in SPMD programming
During the development of a parallel solver for Maxwell equations by integral formulations and Fast Multipole Method (FMM), we needed to optimize a critical part including a lot of communications and computations. Generally, many parallel programs need to communicate, but choosing explicitly the way and the instant may decrease the efficiency of the overall program. So, the overlapping of computations and communications may be a way to reduce this drawback. We will see a implementation of this...
Effective computation of restoring force vector in finite element method
We introduce a new way of computation of time dependent partial differential equations using hybrid method FEM in space and FDM in time domain and explicit computational scheme. The key idea is quick transformation of standard basis functions into new simple basis functions. This new way is used for better computational efficiency. We explain this way of computation on an example of elastodynamic equation using quadrilateral elements. However, the method can be used for more types of elements and...
Efficient computation of enclosures for the exact solvents of a quadratic matrix equation.
Efficient FORTRAN implementation of the gaussian elimination and Householder reduction algorithms on the IBM 3090 vector multiprocessor
Efficient numerical algorithms for balanced stochastic truncation
We propose an efficient numerical algorithm for relative error model reduction based on balanced stochastic truncation. The method uses full-rank factors of the Gramians to be balanced versus each other and exploits the fact that for large-scale systems these Gramians are often of low numerical rank. We use the easy-to-parallelize sign function method as the major computational tool in determining these full-rank factors and demonstrate the numerical performance of the suggested implementation of...
Error control and adaptivity for a phase relaxation model
Error Control and Andaptivity for a Phase Relaxation Model
The phase relaxation model is a diffuse interface model with small parameter ε which consists of a parabolic PDE for temperature θ and an ODE with double obstacles for phase variable χ. To decouple the system a semi-explicit Euler method with variable step-size τ is used for time discretization, which requires the stability constraint τ ≤ ε. Conforming piecewise linear finite elements over highly graded simplicial meshes with parameter h are further employed for space discretization. A posteriori...
Event monitoring of parallel computations
The paper considers the monitoring of parallel computations for detection of abnormal events. It is assumed that computations are organized according to an event model, and monitoring is based on specific test sequences.
Experiments with Krylov subspace methods on a massively parallel computer
In this note, we compare some Krylov subspace iterative methods on the MASPAR, a massively parallel computer with 16K processors. In particular, we apply these methods to solve large sparse nonsymmetric linear systems arising from elliptic partial differential equations. The methods under consideration include conjugate gradient type methods, semiiterative methods, and a hybrid variant. Our numerical results show that, on the MASPAR, one should compare iterative methods rather on the basis of total...
Exponentially convergent parallel discretization methods for the first order evolution equations.
Extrapolation methods for vector sequences.
Factors involved in the performance of computations on Beowulf clusters.
Fast and correctly rounded logarithms in double-precision
This article is a case study in the implementation of a portable, proven and efficient correctly rounded elementary function in double-precision. We describe the methodology used to achieve these goals in the crlibm library. There are two novel aspects to this approach. The first is the proof framework, and in general the techniques used to balance performance and provability. The second is the introduction of processor-specific optimization to get performance equivalent to the best current...
Fast Fourier analysis for over a finite field and related numerical experiments.
Fast multigrid solver
In this paper a black-box solver based on combining the unknowns aggregation with smoothing is suggested. Convergence is improved by overcorrection. Numerical experiments demonstrate the efficiency.
Fast solution of MSC/NASTRAN sparse matrix problems using a multilevel approach.
Fifth-order numerical methods for heat equation subject to a boundary integral specification.