Author: Xiaowei Zhan
Publisher:
ISBN:
Category :
Languages : en
Pages : 230

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Book Description

Author: Ursula van Rienen
Publisher: Springer Science & Business Media
ISBN: 3642568025
Category : Computers
Languages : en
Pages : 387

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Book Description
treated in more detail. They are just specimen of larger classes of schemes. Es sentially, we have to distinguish between semi-analytical methods, discretiza tion methods, and lumped circuit models. The semi-analytical methods and the discretization methods start directly from Maxwell's equations. Semi-analytical methods are concentrated on the analytical level: They use a computer only to evaluate expressions and to solve resulting linear algebraic problems. The best known semi-analytical methods are the mode matching method, which is described in subsection 2. 1, the method of integral equations, and the method of moments. In the method of integral equations, the given boundary value problem is transformed into an integral equation with the aid of a suitable Greens' function. In the method of moments, which includes the mode matching method as a special case, the solution function is represented by a linear combination of appropriately weighted basis func tions. The treatment of complex geometrical structures is very difficult for these methods or only possible after geometric simplifications: In the method of integral equations, the Greens function has to satisfy the boundary condi tions. In the mode matching method, it must be possible to decompose the domain into subdomains in which the problem can be solved analytically, thus allowing to find the basis functions. Nevertheless, there are some ap plications for which the semi-analytic methods are the best suited solution methods. For example, an application from accelerator physics used the mode matching technique (see subsection 5. 4).

Author: Kerry Key
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description
We present a parallel goal-oriented adaptive finite element algorithm that can be used to rapidly compute highly accurate solutions for 2.5D controlled-source electromagnetic (CSEM) and 2D magnetotelluric (MT) modeling problems. We employ unstructured triangular grids to permit efficient discretization of complex modeling domains such as those containing topography, dipping layers and multiple scale structures. Iterative mesh refinement is guided by a goal-oriented error estimator based on a form of dual residual weighting, which is carried out using hierarchical basis computations. Our formulation of the error estimator considers the relative error in the strike aligned fields and their spatial gradients, and therefore results in a more efficient use of mesh vertices than previous error estimators based on absolute field errors. This algorithm is parallelized over frequencies, transmitters, receivers and wave-numbers, where adaptive refinement can be performed in parallel on subsets of these parameters while nearby parameters are able to share the refined grid, thus enabling our algorithm to achieve accurate solutions in run-times of seconds to tens of seconds for realistic models and data parameters when run on cluster computers containing about a thousand processors. Application of this new algorithm to a complex model that includes strong seafloor topography variations and multiple thin stacked reservoirs demonstrates the performance and scalability on a large cluster computer.

Author:
Publisher:
ISBN:
Category : Dissertation abstracts
Languages : en
Pages : 848

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Author: Eric Michael Nelson
Publisher:
ISBN:
Category :
Languages : en
Pages : 312

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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 4

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Book Description
In this project we studied several fundamental issues arising in the parallel adaptive solution of linear and nonlinear elliptic and parabolic PDEs using multilevel algorithms. We focused our attention on a new approach described in the paper ''A New Paradigm for Parallel Adaptive Mesh Refinement'' by Bank and Hoist. The new approach requires almost no communication to solve an elliptic equation in parallel, and therefore has the potential to scale much more efficiently on massively parallel computers than do more traditional algorithms. The algorithm described in the Bank and Hoist paper has an inherently multilevel structure, in that a sequence of problems on a refinement hierarchy of meshes is solved during the course of the calculation. In particular, the algorithm has three main components: (1) We solve a small problem on a coarse mesh, and use a posteriori error estimates to partition the mesh. (2) Each processor is provided the complete coarse mesh and instructed to solve the entire problem, but with its adaptive refinement largely limited to its own assigned mesh partition. (3) A final mesh is computed using the union of the refined partitions provided by each processor. The mesh is regularized into a global conformal mesh, and a final solution is computed using a standard overlapping domain decomposition method or a parallel multigrid method. In certain circumstances the third step can be avoided, leading to an algorithm with no communication beyond that required to synchronize the processors at the beginning of the calculation. We looked at the algorithm closely during the LLNL project in Summer 1999, and we examined algorithms for performing the third step of the algorithm efficiently on massively parallel computers, including parallel multilevel methods and mortar element methods. One result of the summer work at LLNL was a scheme for producing a global conforming mesh in the 3D case through the use of a consistent tie-breaking approach in conjunction with longest-edge simplex bisection. This result completely removes some of the implementation complexity that normally makes the 3D case much more difficult that the 2D case. We presented our work on the parallel algorithm at the Workshop on Iterative Methods held in Livermore in Summer 1999.

Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 702

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Author:
Publisher:
ISBN:
Category : Parallel programming (Computer science)
Languages : en
Pages : 8

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Author: Magdalena Salazar-Palma
Publisher: Artech House Publishers
ISBN:
Category : Mathematics
Languages : en
Pages : 824

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Book Description
Ensure the accuracy of your results when applying the Finite Element Method (FEM) to electromagnetic and antenna problems with this self-contained reference. It provides you with a solid understanding of the method, describes its key elements and numerical techniques, and identifies various approaches to using the FEM in solving real-world microwave field problems.

Author: Francis Piriou
Publisher: John Wiley & Sons
ISBN: 1394276478
Category : Science
Languages : en
Pages : 243

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Book Description
Numerical modeling now plays a central role in the design and study of electromagnetic systems. In the field of devices operating in low frequency, it is the finite element method that has come to the fore in recent decades. Today, it is widely used by engineers and researchers in industry, as well as in research centers. This book describes in detail all the steps required to discretize Maxwell’s equations using the finite element method. This involves progressing from the basic equations in the continuous domain to equations in the discrete domain that are solved by a computer. This approach is carried out with a constant focus on maintaining a link between physics, i.e. the properties of electromagnetic fields, and numerical analysis. Numerous academic examples, which are used throughout the various stages of model construction, help to clarify the developments.