Displaying similar documents to “Parallel methods for solving partial differential equations”

On the preconditioned biconjugate gradients for solving linear complex equations arising from finite elements

Michal Křížek, Jaroslav Mlýnek (1994)

Banach Center Publications

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The paper analyses the biconjugate gradient algorithm and its preconditioned version for solving large systems of linear algebraic equations with nonsingular sparse complex matrices. Special emphasis is laid on symmetric matrices arising from discretization of complex partial differential equations by the finite element method.

Algebraic approach to domain decomposition

Milan Práger (1994)

Banach Center Publications

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An iterative procedure containing two parameters for solving linear algebraic systems originating from the domain decomposition technique is proposed. The optimization of the parameters is investigated. A numerical example is given as an illustration.

A branch&bound algorithm for solving one-dimensional cutting stock problems exactly

Guntram Scheithauer, Johannes Terno (1995)

Applicationes Mathematicae

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Many numerical computations reported in the literature show only a small difference between the optimal value of the one-dimensional cutting stock problem (1CSP) and that of the corresponding linear programming relaxation. Moreover, theoretical investigations have proven that this difference is smaller than 2 for a wide range of subproblems of the general 1CSP.

A fast Lagrangian heuristic for large-scale capacitated lot-size problems with restricted cost structures

Kjetil K. Haugen, Guillaume Lanquepin-Chesnais, Asmund Olstad (2012)

Kybernetika

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In this paper, we demonstrate the computational consequences of making a simple assumption on production cost structures in capacitated lot-size problems. Our results indicate that our cost assumption of increased productivity over time has dramatic effects on the problem sizes which are solvable. Our experiments indicate that problems with more than 1000 products in more than 1000 time periods may be solved within reasonable time. The Lagrangian decomposition algorithm we use does of...