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Corso di Eccellenza ottobre 2007 1 Cell Lab a MATLAB environment for the development of 2D cell method codes Applications of the Cell Method in Engineering Dipartimento Ingegneria Elettrica Politecnico di Torino (ITALY)

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Corso di Eccellenza ottobre 2007 2 Outline Introduction Why MATLAB Philosophy Features Ongoing work Examples electrostatic field magnetostatic field

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Corso di Eccellenza ottobre 2007 3 Introduction Dual lab is not an all-in-one program to solve field problems a program to solve a particular field problem (e.g. electrostatic solver) an established code... but rather it is a collection of MATLAB routines useful to build your own solver an environment for testing and fast-prototyping new formulations a didactical instrument for the Cell Method

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Corso di Eccellenza ottobre 2007 4 Why MATLAB Why MATLAB? It is easy to use Many built-in functions Powerful postprocessing capabilities but, above all MATLAB has very efficient routines to handle sparse matrices

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Corso di Eccellenza ottobre 2007 5 Philosophy MATLAB-like implementation Use exactly the primal (dual) cycle Solving system can be built by using (sparse) matrix operations e.g. for electrostatic problems primal cycle unknown known

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Corso di Eccellenza ottobre 2007 6 Philosophy open source, downlodable and editable does not require any extra MATLAB toolbox (e.g. PDE) encourage the exchanges among researchers

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Corso di Eccellenza ottobre 2007 7 Features 2D mesh import quadrangle diagonal constitutive matrix triangle requires the definition of shape functions nondiagonal sparse constitutive matrix

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Corso di Eccellenza ottobre 2007 8 Features Preprocessor data structure with primal mesh information data structure with dual mesh information build incidence matrices (0, +1, -1) boundary conditions Solver: MATLAB built-in functions factorization ( lu, chol, qr, luinc ) direct methods ( \ operator) iterative methods ( bicg, bicgstab, cgs, gmres, lsqr, minres, pcg, qmr, symmlq ) Postprocessor standard MATLAB tool customized routines

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Corso di Eccellenza ottobre 2007 9 Ongoing work implementation of a quadrangular mesh generator import of MATLAB based simplex mesh generator DISTMESH ( www-math.mit.edu/~persson/mesh/ ) extension to 3D problems (hexaedra and tetraedra) thorough phase of testing new formulations in different application fields

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