A grid based subtree-subcube assignment strategy for solving PDEs on hypercubes
نویسندگان
چکیده
We propose a grid based subtree-subcube assignment strategy for using nested dissection in solving PDE problems on hypercubes. A complexity analysis is given for both our approach and the standard subtree-subcube assignment. The new assignment reduces communication cost by a factor of 0 (logp) in start ups and a factor of about two in traffic volume. This grid based assignment strategy achieves the optimal order in both traffic volume and start ups, it provides load balancing and as much parallelism as is inherent in the algorithm formulation. • Work supported in part by National Science Foundation grant CCR·8619817. ... Work supported in part by the Air Force Office of Scientific Research grant, 88·0243 and lhe Strategic Defense lniLiative Office contract DAAL03-86·K·OI06.
منابع مشابه
Solving Linear Systems with Sparse Matrices on Hypercubes
We investigate parallel Gauss elimination for sparse matrices, especially those arising from the discretization of PDEs. We propose an approach which combines minimum degree ordering, nested dissection, domain decomposition and multifront techniques. Neither symbolic factorization nor explicit representation of elimination trees are needed. An effective and economic dynamic data structure is pr...
متن کاملA BROADCAST CUBE-BASED Ib'IULTIPROCESSOR ARCHITECTURE FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS
A large number of mathematical models in engineering and physical sciences employ Partial Differential Equations (PDEs). The sheer number of operations required in numerically integrating PDEs in these applications has motivated the search for faster methods of computing. The conventional uniprocessor computers are often unable to fulfill the performance requirements for these computation inten...
متن کاملImpact of Physical/Logical Network Topology on Parallel Matrix Computation
In this work, the impact of physical/logical network topol-ogy on parallel matrix computation is studied on an Intel Touchstone DELTA mesh and three generations of hyper-cube multiprocessors. These machines are representative of the continued development of distributed-memory message-passing multiprocessors in the current decade. As the processor architecture and the network hardware continue t...
متن کاملSubcube Fault Tolerance in Hypercube Multiprocessors
In this paper, we study the problem of constructing subcubes in faulty hypercubes. First a divide-and-conquer technique is used to form the set of disjoint subcubes in the faulty hypercube. The concept of irregular subcubes is then introduced to take advantage of advanced switching techniques, such as wormhole routing, to increase the sizes of the available subcubes. We present a subcube partit...
متن کاملUsing Chebyshev polynomial’s zeros as point grid for numerical solution of nonlinear PDEs by differential quadrature- based radial basis functions
Radial Basis Functions (RBFs) have been found to be widely successful for the interpolation of scattered data over the last several decades. The numerical solution of nonlinear Partial Differential Equations (PDEs) plays a prominent role in numerical weather forecasting, and many other areas of physics, engineering, and biology. In this paper, Differential Quadrature (DQ) method- based RBFs are...
متن کامل