Parallel Solution of Reaction-diiusion Equations with a Stabilization Method
نویسنده
چکیده
We present a method for the computation of stable and unstable solutions of a discretized reaction-diiusion equation. Fixed point solvers are frequently used for this problem. But they diverge for many applications. A method for the stabilization of these solvers has been introduced in 3] and 6]. This (sequential) method is now modiied so that the algorithm allows for parallel execution. The parallelization is done on a high level and enables the simultaneous execution of the main algorithmic blocks.
منابع مشابه
A Characteristic Domain Splitting
This work treats a linear convection-diiusion problem. Diiusion and convection may be equally important or convection may dominate the problem. The method of characteristics is combined with an overlapping domain decomposition technique so that domain decomposition is naturally combined with the time stepping. In each time step, the algorithm rst determines the characteristic solution. Then a d...
متن کاملMixed Finite-element Solution of Reaction-diiusion Equations Using a Two-grid Method
We present a method for solving nonlinear reaction-diiusion equations, s @p @t ? r (Krp) = f (p); using a mixed nite-element method. To linearize the mixed-method equations , we use a two-grid scheme that relegates all of the Newton-like iterations to grids much coarser than the original one, with no loss in order of accuracy. The use of a multigrid-based solver for the indeenite linear systems...
متن کاملAn Example for Parallel Scarc and Its Application to the Incompressible Navier-stokes Equations
We present a general multigrid approach for the parallel solution of discretized Poisson-or convection{diiusion-like equations. Both are necessary subproblems in the numerical solution process of the incompressible Navier-Stokes equations via projection methods. Our approach leads to high parallel eeciency and excellent convergence rates, even on very anisotropic meshes, as characteristic for c...
متن کاملA Comparison of Two Numerical Methodsfor Oscillatory Reaction - Di usion SystemsJ
|Reaction-diiusion systems whose kinetics contain a stable limit cycle are an established class of models for a range of oscillatory biological and chemical phenomena. In this paper, the author compares two numerical methods for calculating the oscillatory wake solutions generated by spatially localized perturbations for one particular reaction-diiusion system, of-! type. The two methods are a ...
متن کاملZurich ̈ Technische Hochschule
We present PARDISO, a new scalable parallel sparse direct linear solver on shared memory multiprocessors. In this paper, we describe the parallel fac-torization algorithm which utilizes the supernode structure of the matrix to reduce the number of memory references with Level 3 BLAS. We also propose enhancements that signiicantly reduce the communication rate for pipelining parallelism. The res...
متن کامل