1. 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)

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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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