Download Algorithms for Elliptic Problems: Efficient Sequential and by Marián Vajtersic PDF

By Marián Vajtersic

This quantity bargains with difficulties of recent powerful algorithms for the numerical answer of the main usually happening elliptic partial differential equations. From the perspective of implementation, cognizance is paid to algorithms for either classical sequential and parallel computers.
the 1st chapters are dedicated to speedy algorithms for fixing the Poisson and biharmonic equation. within the 3rd bankruptcy, parallel algorithms for version parallel computers of the SIMD and MIMD varieties are defined. The implementation points of parallel algorithms for fixing version elliptic boundary worth difficulties are defined for platforms with matrix, pipeline and multiprocessor parallel desktop architectures. a latest and renowned multigrid computational precept which deals a very good chance for a parallel recognition is defined within the subsequent bankruptcy. extra parallel variations dependent during this concept are provided, wherein equipment and assignments thoughts for hypercube platforms are handled in additional element. The final bankruptcy offers VLSI designs for fixing targeted tridiagonal linear platforms of equations coming up from finite-difference approximations of elliptic difficulties.
For researchers drawn to the improvement and alertness of quick algorithms for fixing elliptic partial differential equations utilizing complex desktops.

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Extra resources for Algorithms for Elliptic Problems: Efficient Sequential and Parallel Solvers

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V are N 2 -dimensional vectors. er 1 38 that the first ]J points belong to öQ n Rh. Then the matrix M can be considered in the form where Mt and M 2 have dimensions pX N 2 and (N 2-p) X N 2, respectively. 58) where The matrix BI is of dimension p X N2 and has the form BI = [1,0], where 1 is the unit matrix of order p. 58). trix C = BI M-t B[ of dimension ]J X P is compllted. In order to solve effectively the system with Illatrix C, the componcllts of ils triangular decomposi ti on may be computed in this phase as weIl.

60) To solve this, we may apply the three-Ievel iteration scheme [:33] (ak+lUk+d-1M[u(k+l) - k = 0, 1, 2, ... 61) where M is a conveniently chosen easily invertibl(~ matrix and ak, Uk, k = 1, 2, ... , are parameters guaranteping eonvprgenep of the iteration process. In the method of flctive unknowns, L is a bloek upper triangular matrix. 61). However, deeper research into the theory of iteration methods in subspaces (the so-ealled symmetrizing iteration sehemes in [28, 29]) made it possible to aehieve new results that have been employed also in the methods of fietive unknowus.

X,:) +~ ,:) u,T . Y ) with Dirichlet boundary value conditions, the number of necessary operations is O( h2 ln [-1) with h being the discretization step. 4 Method of decomposition Consider an L-shaped domain R as sketched ill Fig. 63) n 8R(2)). er 1 ilR (2) R,,(2) Fig. 5. u :::: fis replaced by u :::: gon the common boundary. 56). 64 ) u(i) :::: 9 on DR(i),i :::: 1,2. ors whose components correspond to the points of the grid Rh( 1) alld Rh( 2), respectively. The matrices E and F correspond to the five-point approximation on the subdomains and the matrix S represents the functional elependence between the components of the solution.

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