The construction of preconditioners for elliptic problems by substructuring. I
Mathematics of Computation
Iterative methods for the solution of elliptic problems on regions partitioned into substructures
SIAM Journal on Numerical Analysis
Analysis of preconditioners for domain decomposition
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific and Statistical Computing
Performance of scientific software
Mathematical aspects of scientific software
Convergence of O(h4) cubic spline collocation methods for elliptic partial differential equations
SIAM Journal on Numerical Analysis
A robust parallel solver for block tridiagonal systems
ICS '88 Proceedings of the 2nd international conference on Supercomputing
A parallel spline collocation-capacitance method for elliptic partial differential equations
ICS '88 Proceedings of the 2nd international conference on Supercomputing
Introduction to Parallel & Vector Solution of Linear Systems
Introduction to Parallel & Vector Solution of Linear Systems
A Schwarz splitting variant of cubic spline collocation methods for elliptic PDEs
C3P Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2
Finite element solution of boundary value problems: theory and computation
Finite element solution of boundary value problems: theory and computation
Schwarz splitting and template operators
Schwarz splitting and template operators
Spline collocation methods, software and architectures for linear elliptic boundary value problems
Spline collocation methods, software and architectures for linear elliptic boundary value problems
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We are interested in the efficient solution of linear second order Partial Differential Equation (PDE) problems on rectangular domains. The PDE discretisation scheme used is of Finite Element type and is based on quadratic splines and the collocation methodology. We integrate the Quadratic Spline Collocation (QSC) discretisation scheme with a Domain Decomposition (DD) technique. We develop DD motivated orderings of the QSC equations and unknowns and apply the Preconditioned Conjugate Gradient (PCG) method for the solution of the Schur Complement (SC) system. Our experiments show that the SC-PCG-QSC method in its sequential mode is very efficient compared to standard direct band solvers for the QSC equations. We have implemented the SC-PCG-QSC method on the iPSC/2 hypercube and present performance evaluation results for up to 32 processors configurations. We discuss a type of nearest neighbour communication scheme, in which the amount of data transfer per processor does not grow with the number of processors. The estimated efficiencies are at the order of 90%.