... InProceedings{pg_cray, author = {Peter Gottschling and Wolfgang E. Nagel and Matthias Tief}, ... more ... InProceedings{pg_cray, author = {Peter Gottschling and Wolfgang E. Nagel and Matthias Tief}, title = {Domain ... Springer. @inproceedings{jarvi:99:binders, author = {J. J\"arvi}, title = {{C++} Function Object Binders Made Easy}, conflocation = {Erfurt, Germany}, month = aug ...
We describe and evaluate a numerical solution strategy for simulating surface acoustic waves thro... more We describe and evaluate a numerical solution strategy for simulating surface acoustic waves through semiconductor devices with complex geometries. This multi-physics problem is of particular relevance to the design of quantum electronic devices. The mathematical model consists of two coupled partial differential equations for the elastic wave propagation and the electric field, respectively, in anisotropic piezoelectric media. These equations are discretized by the finite element method in space and by a finite difference method in time. The latter method yields a convenient numerical decoupling of the governing equations. We describe how a computer implementation can utilize the decoupling and via object-oriented programming techniques reuse independent codes for the Poisson equation and the linear time-dependent elasticity equation. First we apply the simulator to a simplified model problem for verifying the implementation, and thereafter we show that the methodology is capable of simulating a real-world case from nanotechnology, involving surface acoustic waves in a geometrically non-trivial device made of Gallium Arsenide.
This paper contains a thorough investigation of the numerical accuracy and efficiency of an overl... more This paper contains a thorough investigation of the numerical accuracy and efficiency of an overlapping domain decomposition (Schwarz iteration) method for weakly dispersive and non-linear water waves. The investigation is restricted to one-dimensional wave propagation. In our tests, a global domain is divided into two overlapping subdomains. A local boundary value problem (at a time level) is solved in each subdomain, with boundary values extracted from the neighboring domains. The size of the overlap and number of iterations over the domains are the principal parameters that influence the convergence speed and numerical accuracy. We also investigate different finite difference and finite element formulations. The finite signal speed in wave problems makes domain decomposition methods particularly efficient, and the proposed method converges satisfactorily already for an overlap of some typical water depths and a few (2-3) iterations. Numerical artifacts and instabilities may develop at the subdomain boundaries for certain choices of overlap, wave lengths, grid sizes, and (discrete) wave velocities. A special filtering technique is designed to make the method more robust with respect to such instabilities.
Proceedings of the 8th International Conference on Applied Parallel Computing State of the Art in Scientific Computing, Jun 18, 2006
Computational Fluid Dynamics (CFD) is an important research field with a broad spectrum, requirin... more Computational Fluid Dynamics (CFD) is an important research field with a broad spectrum, requiring a close interplay between mathematical modeling, numerical methods, software development, and high performance computing. Programming CFD applications is an inherently difficult task due to many factors related to numerics and software. For modern CFD applications, use of parallel computers is a must, which makes the CFD code development even more challenging. Rapid and flexible programming of a parallel CFD application calls for re-usable serial and parallel software components plus a modular overall parallel framework that allows an easy coupling between different components. Moreover, more attention needs to be put on securing the performance of the software components. This minisymposium thus attempts to shed some light into the recent developments in respect of CFD-related numerical methods, programming techniques and software libraries.
... InProceedings{pg_cray, author = {Peter Gottschling and Wolfgang E. Nagel and Matthias Tief}, ... more ... InProceedings{pg_cray, author = {Peter Gottschling and Wolfgang E. Nagel and Matthias Tief}, title = {Domain ... Springer. @inproceedings{jarvi:99:binders, author = {J. J\"arvi}, title = {{C++} Function Object Binders Made Easy}, conflocation = {Erfurt, Germany}, month = aug ...
We describe and evaluate a numerical solution strategy for simulating surface acoustic waves thro... more We describe and evaluate a numerical solution strategy for simulating surface acoustic waves through semiconductor devices with complex geometries. This multi-physics problem is of particular relevance to the design of quantum electronic devices. The mathematical model consists of two coupled partial differential equations for the elastic wave propagation and the electric field, respectively, in anisotropic piezoelectric media. These equations are discretized by the finite element method in space and by a finite difference method in time. The latter method yields a convenient numerical decoupling of the governing equations. We describe how a computer implementation can utilize the decoupling and via object-oriented programming techniques reuse independent codes for the Poisson equation and the linear time-dependent elasticity equation. First we apply the simulator to a simplified model problem for verifying the implementation, and thereafter we show that the methodology is capable of simulating a real-world case from nanotechnology, involving surface acoustic waves in a geometrically non-trivial device made of Gallium Arsenide.
This paper contains a thorough investigation of the numerical accuracy and efficiency of an overl... more This paper contains a thorough investigation of the numerical accuracy and efficiency of an overlapping domain decomposition (Schwarz iteration) method for weakly dispersive and non-linear water waves. The investigation is restricted to one-dimensional wave propagation. In our tests, a global domain is divided into two overlapping subdomains. A local boundary value problem (at a time level) is solved in each subdomain, with boundary values extracted from the neighboring domains. The size of the overlap and number of iterations over the domains are the principal parameters that influence the convergence speed and numerical accuracy. We also investigate different finite difference and finite element formulations. The finite signal speed in wave problems makes domain decomposition methods particularly efficient, and the proposed method converges satisfactorily already for an overlap of some typical water depths and a few (2-3) iterations. Numerical artifacts and instabilities may develop at the subdomain boundaries for certain choices of overlap, wave lengths, grid sizes, and (discrete) wave velocities. A special filtering technique is designed to make the method more robust with respect to such instabilities.
Proceedings of the 8th International Conference on Applied Parallel Computing State of the Art in Scientific Computing, Jun 18, 2006
Computational Fluid Dynamics (CFD) is an important research field with a broad spectrum, requirin... more Computational Fluid Dynamics (CFD) is an important research field with a broad spectrum, requiring a close interplay between mathematical modeling, numerical methods, software development, and high performance computing. Programming CFD applications is an inherently difficult task due to many factors related to numerics and software. For modern CFD applications, use of parallel computers is a must, which makes the CFD code development even more challenging. Rapid and flexible programming of a parallel CFD application calls for re-usable serial and parallel software components plus a modular overall parallel framework that allows an easy coupling between different components. Moreover, more attention needs to be put on securing the performance of the software components. This minisymposium thus attempts to shed some light into the recent developments in respect of CFD-related numerical methods, programming techniques and software libraries.
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