An application of the boundary element method to the magnetic field integral equation

Ingber, M. S.; Ott, R. H.

doi:10.1109/8.81487

Cited by 23 publications

(16 citation statements)

References 10 publications

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“…If, however, the order of the geometric shape function is greater than the order of approximation of the fields, then the geometric elements are called superparametric; conversely, the geometric elements are called subparametric if their order is less than that of the field shape elements [9]. There are advantages to using different orders of approximation of the geometry and fields.…”

Section: Discretization Of the Boundary-integral Operatorsmentioning

confidence: 99%

“…There are advantages to using different orders of approximation of the geometry and fields. Ingber and Ott [9] have gotten good results when approximating the geometry to second order, while approximating the currents with linear shape functions. This means that there may be fewer variables required to represent the field than to represent the geometry, with a consequent reduction in computer resources to solve for the fields.…”

Section: Discretization Of the Boundary-integral Operatorsmentioning

confidence: 99%

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Boundary-Integral Equations in Eddy-Current Calculations

Murphy

Sabbagh

1995

Review of Progress in Quantitative Nondestructive Evaluation

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Volume-integral equations have proven to be very successful in the computation of eddy-current probe-flaw responses for NDE problems having a number of simple geometries. This approach to NDE computations has proven superior to the finite-element approach in both accuracy and computer resources required, and is the basis of our proprietary code VIC-3Dl. The volume-integral approach, however, is not as well adapted to accommodating the complex geometries sometimes required in practical applications. An example is the separation of edge and corner effects from the response of a flaw. We will discuss an extension of the volume-integral approach that incorporates boundary-integral equations to provide a description of complicated surface geometries. BACKGROUND

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Section: Discretization Of the Boundary-integral Operatorsmentioning

confidence: 99%

Section: Discretization Of the Boundary-integral Operatorsmentioning

confidence: 99%

Boundary-Integral Equations in Eddy-Current Calculations

Murphy

Sabbagh

1995

Review of Progress in Quantitative Nondestructive Evaluation

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“…When edge and corner nodes have Dirichlet boundary conditions for at least 2 duplicate nodes, off functional node collocation is required to avoid singularities in the discretized linear system of equations [4]. The DirichletEdgeNode class has one additional property: char side; //The edge side of element…”

Section: Structure Of the Object-oriented C++ Solutionmentioning

confidence: 99%

“…Historically, BEM codes have been written in FORTRAN to solve a variety of problems including potential problems [9], vorticity formulations [3], and the magnetic field integral equation [4]. More recently, object-oriented implementations of the BEM has been discussed in the literature as a means for writing solutions that are easier to read and maintain.…”

Section: Introductionmentioning

confidence: 99%

Object-oriented C++ boundary element solution of the vector Laplace equation

Ingber

2010

Boundary Elements and Other Mesh Reduction Methods XXXII

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The Boundary Element Method (BEM) lends itself well to an object-oriented implementation. Well-defined class hierarchies can reduce the size of a problem solution while improving the readability and maintainability of the solution. The BEM uses geometric elements, defined as collections of nodes, to model a surface. Boundary conditions, specified by the problem, are defined at each node. This suggests an object oriented solution that defines a base Element class that can be extended to define triangular elements and quadrilateral elements, and a base Node class that can be extended to define more specialized nodes, such as edge and corner nodes. Historically, BEM codes have been written in FORTRAN 90 and object oriented codes have been deemed too slow for such computationally intensive solutions. In this paper I will discuss the development and optimization of an object-oriented BEM code, written in C++, for solving the vector Laplace equation for the magnetic vector potential in three dimensions. The solution to the 3-D magnetic field problem was first written and tested in FORTRAN 90. Due to the complexity and size of the problem solution, the translation to C++ went through several stages. At each stage the code was tested for accuracy and speed. After optimization of the C++ code, which included optimization of memory allocation, optimization of class structures, optimization of functions required to build the discretized linear system of equations and optimization of the solver, the C++ code executed faster than the FORTRAN 90 code for all test problems.

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“…The standard nodal based boundary element method does not provide a rigorous description of the tangential surface currents especially near corners and edges, because of the ambiguity in normal directions. Semi-discontinuous superparametric elements can be used [3]. Also, discretization of the integral equation is central to couple the source fields into the materials and flaws.…”

Section: Introductionmentioning

confidence: 99%