The time-dependent vibration of forced floating elastic plates by eigenfunction matching in two and three dimensions

Wave Motion ◽  
2019 ◽  
Vol 88 ◽  
pp. 21-33 ◽  
Author(s):  
Michael H. Meylan
Keyword(s):  
Three Dimensions ◽  
Time Dependent ◽  
Elastic Plates

The time-dependent Schrödinger equation in three dimensions under geometric constraints

2019 ◽  
Vol 60 (3) ◽  
pp. 032101 ◽  
Author(s):  
Irina Petreska ◽  
Antonio S. M. de Castro ◽  
Trifce Sandev ◽  
Ervin K. Lenzi
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Geometric Constraints ◽  
Three Dimensions ◽  
Time Dependent

Asymptotic and Exact Radiation Boundary Conditions for Time-Dependent Scattering

1999 ◽  
Author(s):  
Lonny L. Thompson ◽  
Runnong Huan
Keyword(s):  
Cauchy Problem ◽  
Finite Element ◽  
Boundary Conditions ◽  
Near Field ◽  
Three Dimensions ◽  
Time Dependent ◽  
Radiation Boundary Condition ◽  
Radiation Boundary Conditions ◽  
First Order ◽  
Radiation Boundary

Abstract Asymptotic and exact local radiation boundary conditions first derived by Hagstrom and Hariharan are reformulated as an auxiliary Cauchy problem for linear first-order systems of ordinary equations on the boundary for each harmonic on a circle or sphere in two- or three-dimensions, respectively. With this reformulation, the resulting radiation boundary condition involves first-order derivatives only and can be computed efficiently and concurrently with standard semi-discrete finite element methods for the near-field solution without changing the banded/sparse structure of the finite element equations. In 3D, with the number of equations in the Cauchy problem equal to the mode number, this reformulation is exact. If fewer equations are used, then the boundary conditions form uniform asymptotic approximations to the exact condition. Furthermore, using this approach, we formulate accurate radiation boundary conditions for the two-dimensional unbounded problem on a circle. Numerical studies of time-dependent radiation and scattering are performed to assess the accuracy and convergence properties of the boundary conditions when implemented in the finite element method. The results demonstrate that the new formulation has dramatically improved accuracy and efficiency for time domain simulations compared to standard boundary treatments.

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