The method of acceleration of solving equations system in case of shape and/or boundary conditions changes

Norbert Sczygiol, Juliusz Mikoda

Institute of Computer and Information Sciences, Czestochowa University of Technology,ul. Dąbrowskiego 73, 42-200 Częstochowa, Poland.

DOI:

https://doi.org/10.7494/cmms.2011.2.0360

Abstract:

This paper presents new approach to the problem of conducting numerical simulations in case of applying shape and/or boundary conditions changes resulting from technological and/or constructional modifications. Presented approach allows to shorten the time required for solving linear equations system by using results obtained from simulation for original model (before modifications) to initialize vector of solution in the second turn of computation (for modified model). The conjugate gradient method was used to solve the system of equations. The paper presents results of simulations conducted with use of such approach. In the first case model of some constructional element was changed by adding a slot. In the second case, the modification involves changing value of temperature used in boundary conditions. The results obtained in both cases confirm that described method can decrease time required for solving linear system of equations. The costs of such approach are relatively small and does not affect total time of computation. Using the approach described in this paper, in connection with mesh reconstruction, can give significant acceleration. In the analysed cases the total acceleration resulting from the application of these two techniques was approximately 30%.

Cite as:

Sczygiol, N., & Mikoda, J. (2011). The method of acceleration of solving equations system in case of shape and/or boundary conditions changes. Computer Methods in Materials Science, 11(2), 394 – 398. https://doi.org/10.7494/cmms.2011.2.0360

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