Showing papers by "Nathan Ida published in 1994"
Book•
31 Dec 1994
TL;DR: In this article, the electromagnetic field equations are solved using the finite element method and the finite difference method of elliptic processes, with boundary integral, volume integral, and combined formulations.
Abstract: Introduction. The electromagnetic field equations. Analytic methods of solution. The finite difference method. The finite element method. Elliptic partial differential equations. Finite difference solution of elliptic processes. Finite element formulation. Boundary integral, volume integral and combined formulations. Parabolic partial differential equations. Hyperbolic partial differential equations. Miscellaneous numerical methods. Index.
63 citations
TL;DR: The efficiency of the local error estimation technique has been demonstrated by the adaptive refinement of an ac transmission line problem in 2D and an eddy current problem employing complex magnetic vector potential formulation in 3D.
Abstract: A new approach for estimating an 'a posteriori' error locally on an element by element basis for the adaptive refinement of a class of 2D and 3D boundary value problems has been investigated in this paper. It is necessary to have an efficient, robust and reliable error estimator to generate an optimal adaptive mesh. In this work an 'a posteriori' error is computed by solving a local problem on a patch of elements. It is simple to implement and is computationally inexpensive. This method computes the local as well as global error by using a h-version of adaption with quadratic shape functions to solve the local problem. The refinement algorithm makes use of a minimal hierarchical tree based data structure which minimizes the amount of tree traversal normally required during the refinement process. The efficiency of the local error estimation technique has been demonstrated by the adaptive refinement of an ac transmission line problem in 2D and an eddy current problem employing complex magnetic vector potential formulation in 3D. The coarse mesh and the refined optimal meshes and the numerical results substantiate that the local 'a posteriori' error estimate is efficient and simple to use for most practical applications. >
14 citations
TL;DR: The 3D hexahedral edge element is used for two 2D applications in a simple way to compute 2D problems using edge elements without the need to define special 2D finite elements.
Abstract: We present in this paper the use of the 3D hexahedral edge element for two 2D applications. The procedure consists of first computing the 3D hexahedral edge elemental matrix. Then the "reduction" for 2D domains is applied in the assembling process, resulting in a simple way to compute 2D problems using edge elements without the need to define special 2D finite elements. The method maintains all the properties of a 2D method with the exception of the elemental matrix calculation. >
2 citations
TL;DR: Why it is important to be able to return by reference, particularly for large dynamic objects in mathematical applications, is looked at, and a new scheme for doing so is presented that can attain efficiency comparable to that of 'method of reference counting', but without the undesirable side-effects of the latter.
Abstract: It is a well known fact that passing objects into functions by reference (in C++) is more efficient than passing by value. Passing objects, created within functions, out of functions by reference could also be more efficient if it wasn't sure to cause memory-leak in the system. Programmers therefore resort to "pass-by-reference, return-by-value". Here we first briefly look at why it is important to be able to return by reference, particularly for large dynamic objects in mathematical applications, and then present a new scheme for doing so. The new method can attain efficiency comparable to that of 'method of reference counting', but without the undesirable side-effects of the latter.
2 citations
14 Sep 1994
TL;DR: In this paper, a coupled boundary element/finite element approach is used for non-destructive testing of lossy dielectric materials in the open domain, where edge finite elements allow accurate continuity of tangential components of the electric or magnetic field and therefore do not introduce parasitic eigenvalues into the system of equations.
Abstract: Microwave nondestructive testing of lossy dielectric materials involves one of two situations: either the test sample is illuminated and a signal representing the material condition is obtained, or the material is introduced into a cavity and the measurement is done on cavity parameters. In the first case, the major problem is calculating and identifying modes in the cavity and avoiding spurious solutions. The second requires solution in the open domain and is treated here by coupled boundary element/finite element approach. The two methods are used: one uses a rather standard edge element solution and scanning of frequency to detect resonance. The second formulation is based on curvilinear edge elements which avoids spurious modes. The edge finite elements allow accurate continuity of tangential components of the electric or magnetic field and therefore do not introduce parasitic eigenvalues into the system of equations. Examples of scattering by lossy dielectrics and of loaded cavity resonators are given. These include scattering cross section of bodies and propagation in composite materials.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.