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Effective computation of restoring force vector in finite element method

Martin Balazovjech, Ladislav 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 Balazovjech, Ladislav 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...

Elastic wave propagation in parallel: the Huygens' approach.

Javier Sabadell (2002)

Revista Matemática Complutense

The use of parallel computers makes it feasible to simulate elastic waves throughout large heterogeneous structures, and new domain decomposition methods can be used to increase their efficiency and decrease the computing time spent in the simulation. In this paper we introduce a simple parallel algorithm for the propagation of elastic waves in complex heterogeneous media after a finite element discretization. This method performs more efficiently than classic domain decomposition techniques based...

Explicit integration of equations of motion solved on computer cluster

Rek, Václav (2019)

Programs and Algorithms of Numerical Mathematics

In the last decade the dramatic onset of multicore and multi-processor systems in combination with the possibilities which now provide modern computer networks have risen. The complexity and size of the investigated models are constantly increasing due to the high computational complexity of computational tasks in dynamics and statics of structures, mainly because of the nonlinear character of the solved models. Any possibility to speed up such calculation procedures is more than desirable. This...

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