Parallel Methods for Parabolic Equations Based on MPI Implementation

Parallel Domain Decomposition Methods for Parabolic Equations

On the Implementation of Exponential Methods for Semilinear Parabolic Equations

The time integration of semilinear parabolic problems by exponential methods of different kinds is considered. A new algorithm for the implementation of these methods is proposed. The algorithm evaluates the operators required by the exponential methods by means of a quadrature formula that converges like O(e−cK/ ln K), with K the number of quadrature nodes. The algorithm allows also the evalua...

MPIPOV: A Parallel Implementation of POV-Ray Based on MPI

The work presents an MPI parallel implementation of Pov-Ray, a powerful public domain ray tracing engine. The major problem in ray tracing is the large amount of CPU time needed for the elaboration of the image. With this parallel version it is possible to reduce the computation time or to render, with the same elaboration time, more complex or detailed images. The program was tested successful...

Numerical Methods for Parabolic Equations

(1)  ut −∆u = f in Ω× (0, T ), u = 0 on ∂Ω× (0, T ), u(·, 0) = u0 in Ω. Here u = u(x, t) is a function of spatial variable x ∈ Ω and time variable t ∈ (0, T ). The Laplace differential operator ∆ is taking with respect to the spatial variable. For the simplicity of exposition, we consider only homogenous Dirichlet boundary condition and comment on the adaptation to Neumann and other type of b...

Implementation and Evaluation of MPI-Based Parallel MD Program

The message-passing interface (MPI)-based object-oriented particle–particle interactions (PPI) library is implemented and evaluated. The library can be used in the n-particle simulation algorithm designed for a ring of p interconnected processors. The parallel simulation is scalable with the number of processors, and has the time requirement proportional to n2/p if n/p is large enough, which gu...