A distributed memory parallel element-by-element scheme for semiconductor device simulation

Bova, Steven W.; Carey, G. F.

doi:10.1016/s0045-7825(99)00181-4

Cited by 13 publications

(9 citation statements)

References 22 publications

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“…Decompression, however, is unacceptable since the size of the original matrix might be orders of magnitude larger than the available memory. Thus, the block compression methodology must include a strategy to use the blocks for solving the system in its compressed form, which is done by using a mapping matrix known as adjacency matrix in the finite element terminology [15] [16]. The adjacency matrix allows the description of the original system matrix in a series where the coefficients are blocks and the basis functions are the adjacency matrices.…”

Section: The Block Transformmentioning

confidence: 99%

On the block wavelet transform applied to the boundary element method

Bucher¹,

Wrobel²,

Mansur³

et al. 2004

Engineering Analysis with Boundary Elements

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This paper follows an earlier work by Bucher et al. [1] on the application of wavelet transforms to the boundary element method, which shows how to reuse models stored in compressed form to solve new models with the same geometry but arbitrary load cases-the so-called virtual assembly technique. The extension presented in this paper involves a new computational procedure created to perform the required twodimensional wavelet transforms by blocks, theoretically allowing the compression of matrices of arbitrary size. Details of the computer implementation that allows the use of this methodology for very large models or at high compression ratios are given. A numerical application shows a standard PC being used to solve a 131,072 DOF model, previously compressed, for 100 distinct load cases in less than 1 hour-or 33 seconds for each load case.

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Section: The Block Transformmentioning

confidence: 99%

On the block wavelet transform applied to the boundary element method

Bucher¹,

Wrobel²,

Mansur³

et al. 2004

Engineering Analysis with Boundary Elements

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show abstract

“…Both overlapping and non-overlapping domain decomposition strategies are applicable. Typically, the subdomain calculations are carried out on their respective processors with overlap or interface communication using MPI between adjacent processors [1,11,23,38]. To date there has been little use of these ideas for device and process simulation except in a few university research studies [61,77], but they are now widely used for other engineering applications.…”

Section: Parallel and Distributed Computingmentioning

confidence: 99%

“…A representative example is included here from a recent study. The test problem was the n-channel depleted MOSFET described in [11] using the drift-diffusion model on a mesh of 7722 triangles generated by Delaunay triangulation. A partitioning of the unstructured grid to 6 subdomains is indicated in Figure 5.…”

Section: Parallel and Distributed Computingmentioning

confidence: 99%

Advanced Numerical Methods and Software Approachesfor Semiconductor Device Simulation

1999

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In this article we concisely present several modern strategies that are applicable to driftdominated carrier transport in higher-order deterministic models such as the driftdiffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of “upwind” and artificial dissipation schemes, generalization of the traditional Scharfetter – Gummel approach, Petrov – Galerkin and streamline-upwind Petrov Galerkin (SUPG), “entropy” variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of the methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. We have included numerical examples from our recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and we emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, we briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.

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“…[9] and [28], the SBS approach is used as a complementary procedure for a DD method, while in [24] a fully SBS scheme is developed for the solution of the unsteady incompressible Navier-Stokes equations, though the term SBS is not explicitly used. Another interesting work that uses this approach is given in [12].…”

Section: Introductionmentioning

confidence: 99%

“…Also, a large number of EBE based preconditioners is available in literature. We may cite the works of Bova and Carey [12] and Gullerud and Dodds [13] as examples of MPI-based SBS implementations using EBE schemes. Okuda et al [25] presents an EBE scheme for massively parallel computers.…”

Section: Introductionmentioning

confidence: 99%

Parallel implementation of the finite element method using compressed data structures

Ribeiro

Ferreira

2007

Comput Mech

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This paper presents a parallel implementation of the finite element method designed for coarsegrain distributed memory architectures. The MPI standard is used for message passing and tests are run on a PC cluster and on an SGI Altix 350. Compressed data structures are employed to store the coefficient matrix and obtain iterative solutions, based on Krylov methods, in a subdomain-by-subdomain approach. Two mesh partitioning schemes are compared: non-overlapping and overlapping. The pros and cons of these partitioning methods are discussed. Numerical examples of symmetric and non-symmetric problems in two and three dimensions are presented.

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A distributed memory parallel element-by-element scheme for semiconductor device simulation

Cited by 13 publications

References 22 publications

On the block wavelet transform applied to the boundary element method

On the block wavelet transform applied to the boundary element method

Advanced Numerical Methods and Software Approachesfor Semiconductor Device Simulation

Parallel implementation of the finite element method using compressed data structures

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