Dynamics with Matrices Possessing Kronecker Product Structure | Zendy

Marcin Łoś | Zendy; Maciej Woźniak | Zendy; Maciej Paszyński | Zendy; Lisandro Dalcín | Zendy; Victor M. Calo | Zendy

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Dynamics with Matrices Possessing Kronecker Product Structure

Author(s) -

Marcin Łoś,

Maciej Woźniak,

Maciej Paszyński,

Lisandro Dalcín,

Victor M. Calo

Publication year - 2015

Publication title -

procedia computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.334

H-Index - 76

ISSN - 1877-0509

DOI - 10.1016/j.procs.2015.05.243

Subject(s) - computer science , kronecker product , kronecker delta , backward euler method , finite element method , time stepping , mathematics , isogeometric analysis , elasticity (physics) , stability (learning theory) , algorithm , mathematical optimization , euler equations , discretization , mathematical analysis , physics , materials science , quantum mechanics , machine learning , composite material , thermodynamics

In this paper we present an application of Alternating Direction Implicit (ADI) algorithm for solution of non-stationary PDE-s using isogeometric finite element method. We show that ADI algorithm has a linear computational cost at every time step. We illustrate this approach by solving two example non-stationary three-dimensional problems using explicit Euler and Newmark time-stepping scheme: heat equation and linear elasticity equations for a cube. The stability of the simulation is controlled by monitoring the energy of the solution

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