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Numrering	Referens	Omslagsbild	Hitta
1.	Eriksson, Gustav, et al. (författare) Boundary and interface methods for energy stable finite difference discretizations of the dynamic beam equation 2023 Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 476 Tidskriftsartikel (refereegranskat)abstract We consider energy stable summation by parts finite difference methods (SBP-FD) for the homogeneous and piecewise homogeneous dynamic beam equation (DBE). Previously the constant coefficient problem has been solved with SBP-FD together with penalty terms (SBP-SAT) to impose boundary conditions. In this work, we revisit this problem and compare SBP-SAT to the projection method (SBP-P). We also consider the DBE with discontinuous coefficients and present novel SBP-SAT, SBP-P, and hybrid SBP-SAT-P discretizations for imposing interface conditions. To demonstrate the methodology for two-dimensional problems, we also present a discretization of the piecewise homogeneous dynamic Kirchoff-Love plate equation based on the hybrid SBP-SAT-P method. Numerical experiments show that all methods considered are similar in terms of accuracy, but that SBP-P can be more computationally efficient (less restrictive time step requirement for explicit time integration methods) for both the constant and piecewise constant coefficient problems.

Eriksson, Gustav, et al. (författare)
Boundary and interface methods for energy stable finite difference discretizations of the dynamic beam equation
2023
Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 476
Tidskriftsartikel (refereegranskat)abstract
- We consider energy stable summation by parts finite difference methods (SBP-FD) for the homogeneous and piecewise homogeneous dynamic beam equation (DBE). Previously the constant coefficient problem has been solved with SBP-FD together with penalty terms (SBP-SAT) to impose boundary conditions. In this work, we revisit this problem and compare SBP-SAT to the projection method (SBP-P). We also consider the DBE with discontinuous coefficients and present novel SBP-SAT, SBP-P, and hybrid SBP-SAT-P discretizations for imposing interface conditions. To demonstrate the methodology for two-dimensional problems, we also present a discretization of the piecewise homogeneous dynamic Kirchoff-Love plate equation based on the hybrid SBP-SAT-P method. Numerical experiments show that all methods considered are similar in terms of accuracy, but that SBP-P can be more computationally efficient (less restrictive time step requirement for explicit time integration methods) for both the constant and piecewise constant coefficient problems.

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