Boundary and interface methods for energy stable finite difference discretizations of the dynamic beam equation

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 t...

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Bibliographic Details
Published in:Journal of computational physics Vol. 476; p. 111907
Main Authors: Eriksson, Gustav, Werpers, Jonatan, Niemelä, David, Wik, Niklas, Zethrin, Valter, Mattsson, Ken
Format: Journal Article
Language:English
Published: Elsevier Inc 01.03.2023
Subjects:
Beräkningsvetenskap med inriktning mot numerisk analys
Boundary treatment
Dynamic beam equation
Finite differences
High order methods
Scientific Computing with specialization in Numerical Analysis
Summation by parts
Boundary treatment
High order methods
Finite differences
Summation by parts
Dynamic beam equation
ISSN:0021-9991, 1090-2716, 1090-2716
Online Access:Get full text
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Summary: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. •High order finite difference methods for the dynamic beam equation with discontinuous parameters.•New weak penalty (SAT), strong (projection) and hybrid boundary and interface methods.•The projection method leads to the smallest spectral radius of the spatial operators.
ISSN:0021-9991
1090-2716
1090-2716
DOI:10.1016/j.jcp.2023.111907