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Effective computation of restoring force vector in finite element method

Martin BalazovjechLadislav Halada — 2007

Kybernetika

We introduce a new way of computation of time dependent partial differential equations using hybrid method FEM in space and FDM in time domain and explicit computational scheme. The key idea is quick transformation of standard basis functions into new simple basis functions. This new way is used for better computational efficiency. We explain this way of computation on an example of elastodynamic equation using quadrilateral elements. However, the method can be used for more types of elements and...

Efficient application of e-invariants in finite element method for an elastodynamic equation

Martin BalazovjechLadislav Halada — 2013

Kybernetika

We introduce a new efficient way of computation of partial differential equations using a hybrid method composed from FEM in space and FDM in time domain. The overall computational scheme is explicit in time. The key idea of the suggested way is based on a transformation of standard basis functions into new basis functions. The results of this matrix transformation are e-invariants (effective invariants) with such suitable properties which save the number of arithmetical operations needed for a...

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