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Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The purpose of this paper is to present a modified version of the hybrid Finite Element Method-Dirichlet Boundary Condition Iteration method for the solution of open-boundary skin effect problems.

The modification consists of overlapping the truncation and the integration boundaries of the standard method, so that the integral equation becomes singular as in the well-known Finite Element Method-Boundary Element Method (FEM-BEM) method. The new method is called FEM-SDBCI. Assuming an unknown Dirichlet condition on the truncation boundary, the global algebraic system is constituted by the sparse FEM equations and by the dense integral equations, in which singularities arise. Analytical formulas are provided to compute these singular integrals. The global system is solved by means of a Generalized Minimal Residual iterative procedure.

The proposed method leads to slightly less accurate numerical results than FEM-BEM, but the latter requires much more computing time.

Then FEM-SDBCI appears more appropriate than FEM-BEM for applications which require a shorter computing time, for example in the stochastic optimization of electromagnetic devices.

Note that FEM-SDBCI assumes a Dirichlet condition on the truncation boundary, whereas FEM-BEM assumes a Neumann one.

This paper presents a hybrid finite element — boundary element method for the steady state thermal analysis of energy installations. The coupling of the two techniques is presented: finite elements are used in a bounded region containing thermal sources while the complementary domain is treated with boundary elements. With such a combination the number of unknowns is reduced and an accurate prediction of temperature is obtained. As an example, the temperature rise is computed for the case of three power cables laid in a thermal backfill: the finite element method (FEM) is used for the cables and the backfill while the homogeneous soil is taken into account with the boundary element method (BEM).

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The purpose of this paper is to compare the hybrid FEM-BEM and FEM-DBCI methods for the solution of open-boundary static and quasi-static electromagnetic field problems.

After a brief review of the two methods (both coupling a differential equation for the interior problem with an integral equation for the exterior one), they are compared in terms of accuracy, memory and computing time requirements by means of a set of simple examples.

The comparison suggests that FEM-BEM is more accurate than FEM-DBCI but requires more computing time.

Then FEM-DBCI appears more appropriate for applications which require a shorter computing time, for example in the stochastic optimization of electromagnetic devices. Conversely, FEM-BEM is more appropriate in cases in which a high level of precision is required in a single computation.

Note that the FEM-BEM considered in this paper is a non standard one in which the nodes of the normal derivative on the truncation boundary are placed in positions different from those of the potential.

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

The boundary element method is a useful method for the analysis of field problems involving unbounded regions. Therefore, the method can be used advantageously in combination with the finite element method. This is sometimes called a combination method and it is suitable as a picture‐frame technique. Although this technique attains good accuracy, the matrix of the discretized equation is not banded, since it is a dense matrix. In this paper, we propose an infinite boundary element which divides the unbounded region radially. By the use of this element, the bandwidth of the discretized system matrix does not increase beyond that of the finite element region and its original matrix structure is maintained. The infinite boundary element can also be applied to homogeneous unbounded field problems, for which the Green's function of the mirror image is difficult to use. To illustrate the validity of the proposed technique, some numerical calculations are demonstrated and the results are compared with those of the usual combination method and the method using the hybrid‐type infinite element.

The purpose of this paper is to give a review on the newest developments of high-performance finite element methods (FEMs), and exhibit the recent contributions achieved by the authors’ group, especially showing some breakthroughs against inherent difficulties existing in the traditional FEM for a long time.

Three kinds of new FEMs are emphasized and introduced, including the hybrid stress-function element method, the hybrid displacement-function element method for Mindlin–Reissner plate and the improved unsymmetric FEM. The distinguished feature of these three methods is that they all apply the fundamental analytical solutions of elasticity expressed in different coordinates as their trial functions.

The new FEMs show advantages from both analytical and numerical approaches. All the models exhibit outstanding capacity for resisting various severe mesh distortions, and even perform well when other models cannot work. Some difficulties in the history of FEM are also broken through, such as the limitations defined by MacNeal’s theorem and the edge-effect problems of Mindlin–Reissner plate.

These contributions possess high value for solving the difficulties in engineering computations, and promote the progress of FEM.

This paper aims to extend an efficient method to solve the global system of linear algebraic equations in the hybrid finite element method – boundary element method (FEM‐BEM) solution of open‐boundary skin effect problems. The extension covers the cases in which the skin effect problem is set in a truncated domain in which no homogeneous Dirichlet conditions are imposed.

The extended method is based on use of the generalized minimal residual (GMRES) solver, which is applied virtually to the reduced system of equations in which the unknowns are the nodal values of the normal derivative of the magnetic vector potential on the fictitious truncation boundary. In each step of the GMRES algorithm the FEM equations are solved by means of the standard complex conjugate gradient solver, whereas the BEM equations are not solved but used to perform fast matrix‐by‐vector multiplications. The BEM equations are written in a non‐conventional way, by making the nodes for the potential non‐coinciding with the nodes for its normal derivative.

The paper shows that the method proposed is very competitive with respect to other methods to solve open‐boundary skin effect problems.

The paper illustrates a new method to solve efficiently skin effect problems in open boundary domains by means of the hybrid FEM‐BEM method.

The purpose of this paper is to study the flow and heat transfer characteristics of a phase transition, melting problem. In this problem, phase transition between solid and liquid takes place within a square enclosure in the presence of natural convection.

The physical problem, described with non-linear partial differential equations, is simulated using a hybrid finite element and element free Galerkin method (FEM/EFGM) approach. In energy conservation equation, the fixed-domain, effective heat capacity method is used to take into account the latent heat of phase change. The governing partial differential equations are solved with a meshfree, EFGM near the phase transition front while in the region away from the front with uniform nodal distribution; problem is simulated with traditional FEM.

A sensitivity analysis of characteristic dimensionless numbers Rayleigh number (Ra), Prandtl number (Pr), Stefan number (ste) is presented in order to investigate their impact on thermal and flow fields. Typically computational times of EFGM are higher than that of FEM. Therefore, by using EFGM only in that portion of physical problem where phase transition occurs, the hybrid FEM/EFGM strategy employed in present paper could reduce the computational time of EFGM while still retaining its accuracy. Also, the consistent performance of the results obtained with this hybrid approach is validated with those already available in literature for some special cases.

The hybrid methodology adopted in this paper, is quite new for solving such type of phase transition problem.