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animation:workshops:2013:pdes [2013/06/07 16:19] sbarends [Efficient solution of large systems of non-linear PDEs in science] |
animation:workshops:2013:pdes [2013/06/11 14:48] sbarends [Summary] |
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| - | ===== Summary ===== | + | ===== Objectives ===== |
| - | Any kind of discretization of PDEs will result in a huge, non-linear system of equations. A whole class of most efficient solution technique for such systems rely on Newton-Krylov (NK) solvers, the iterative use of 2 basic algorithms: the Newton algorithm to find the roots of the non-linear equations and an iterative Krylov method to solve the resulting linear part. Convergence properties of NK methods heavily depend on good preconditioning. – NK methods are used by the entire research community. Our goal is to promote the use of these and related, advanced numerical methods in Lyon and to bridge the gap between numerical mathematics and other exact sciences. | + | Computation and simulation are at the heart of current science. Today, 3D multi-physics, multi-scale simulations are within reach, but also encounter the grand challenge of how to efficiently use massively parallel machines with thousands of processors to solve large non-linear systems of equations. |
| + | A whole class of most efficient solution technique for such systems rely on Newton-Krylov (NK) solvers, the iterative use of 2 basic algorithms: the Newton algorithm to find the roots of the non-linear equations and an iterative Krylov method to solve the resulting linear part. Convergence properties of NK methods heavily depend on a good preconditioning of the matrix defining the linear system. | ||
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| + | NK methods are used by the entire research community. This workshops aims at bringing together experts from different fields of science with people who are developing algorithms, numerical methods and implementing complex numerical methods on massively parallel machines. With this approach, we hope to popularize new efficient computing methods, initiate collaboration among scientists of different research fields, and between applicants and developers of methods. | ||
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| + | ===== Note ===== | ||
| + | This workshop is part of the TOFU European Research Council Project (toward a new generation of multi-dimensional stellar evolution models: the TOol of the FUture) which aims at developing such powerful methods. | ||