Approximation of large data from the finite element analysis allowing fast post-processing

• Efficient methods to visualize the results from finite element analysis and imple-mentation of these methods in post-processing results are described.
• The stored data from finite element analysis are replaced by continuous functions suitable for representation in computer graphics.
• Approximation of data in space and also the approximation in time is used.

The article describes efficient methods to visualize the results from finite element analysis and implementation of these methods in post-processing results. The work is based on premise that computer memory and performance are limited and amount of data processed by complex finite element analysis is enormous. Therefore, some kind of simplification and approximation of resulting data has to be used. Multigrid method was the inspiration for research work and development of post-processor.The stored data from finite element analysis are discrete values. The paper deals with several ways of replacing them by continuous functions suitable for representation in computer graphics, which are different from the approximation functions used in finite element method. Special attention is devoted to approximation errors – difference between these functions. Finite element mesh is decomposed into subdomains with respect to approximation errors. The ways of creating mesh hierarchy are described in details and also the possibilities of nodal value interpolations in simplified mesh are discussed in the text.Besides the approximation of data in space, also the approximation in time is used. Pseudo-code of the approximation algorithm key parts is shown. Various types of approximation functions were investigated to reach the lowest approximation error and the highest compression factor. Results are summarized in the article.