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Purpose Electromagnetic noise of permanent magnet synchronous motor (PMSM) seriously affects the sound quality of electric vehicles (EVs). This paper aims to present a comprehensive process for the electromagnetic noise analysis and optimization of a water-cooled PMSM. Design/methodology/approach First, the noises of an eight-pole 48-slot PMSM in at speeds up to 10,000 rpm are measured. Furthermore, an electromagnetic-structural-acoustic model of the PMSM is established for multi-field coupling simulations of electromagnetic noises. Finally, the electromagnetic noise of the PMSM is optimized by using the multi-objective genetic algorithm, where a multi-objective function related to the slot width of PMSM stator is defined for radial electromagnetic force (REF) optimization. Findings The experimental results show that main electromagnetic noises are the 8n-order (n = 1, 2, 3, …) and 12-order noises. The simulated results show that the REFs are mainly generated by the 8n-order (n = 1, 2, 3, 4, 5, 6) vibrations, especially those of the 8th, 16th, 24th and 32th orders. The 12-order noise is a mechanical noise, which might be caused by the bearings and other structures of the PMSM. Comparing the simulated results before and after optimization, both the REFs and electromagnetic noises are effectively reduced, which suggests that an appropriate design of stator slot is important for reducing electromagnetic noise of the PMSM. Originality/value In view of applications, the methods proposed in this paper can be applied to other types of PMSM for generation mechanism analysis of electromagnetic noise, optimal design of PMSM and thereby noise improvement of EVs.

Purpose Based on the error analysis, the authors proposed a new kind of high accuracy boundary element method (BEM) (HABEM), and for the large-scale problems, the fast algorithm, such as adaptive cross approximation (ACA) with generalized minimal residual (GMRES) is introduced to develop the high performance BEM (HPBEM). It is found that for slender beams, the stress analysis using iterative solver GMRES will difficult to converge. For the analysis of slender beams and thin structures, to enhance the efficiency of GMRES solver becomes a key problem in the development of the HPBEM. The purpose of this paper is study on the preconditioning method to solve this convergence problem, and it is started from the 2D BE analysis of slender beams. Design/methodology/approach The conventional sparse approximate inverse (SAI) based on adjacent nodes is modified to that based on adjacent nodes along the boundary line. In addition, the authors proposed a dual node variable merging (DNVM) preprocessing for slender thin-plate beams. As benchmark problems, the pure bending of thin-plate beam and the local stress analysis (LSA) of real thin-plate cantilever beam are applied to verify the effect of these two preconditioning method. Findings For the LSA of real thin-plate cantilever beams, as GMRES (m) without preconditioning applied, it is difficult to converge provided the length to height ratio greater than 50. Even with the preconditioner SAI or DNVM, it is also difficult to obtain the converged results. For the slender real beams, the iteration of GMRES (m) with SAI or DNVM stopped at wrong deformation state, and the computation failed. By changing zero initial solution to the analytical displacement solution of conventional beam theory, GMRES (m) with SAI or DNVM will not be stopped at wrong deformation state, but the stress error is still difficult to converge. However, by GMRES (m) combined with both SAI and DNVM preconditioning, the computation efficiency enhanced significantly. Originality/value This paper presents two preconditioners: DNVM and a modified SAI based on adjacent nodes along the boundary line of slender thin-plate beam. In the LSA, by using GMRES (m) combined with both DNVM and SAI, the computation efficiency enhanced significantly. It provides a reference for the further development of the 3D HPBEM in the LSA of real beam, plate and shell structures.

Purpose – The purpose of this paper is to research the interaction between multiple bubbles and their noise radiation considering the influence of compressibility. The influences of bubble spacing, initial inner pressure, buoyance and phase difference are presented with different bubbles arrangements. Design/methodology/approach – Based on wave equation, the new boundary integral equation considering the compressibility is given by the matching between prophase and anaphase approximation of bubble motion and solved with boundary element method. The time-domain characteristics of noise induced by multiple bubbles are obtained by the moving boundary Kirchhoff integral equation. With the surface discretization and coordinate transformation, the bubbles surface is treated as a moving deformable boundary and noise source, and the integral is implemented on the surface directly. Findings – Numerical results show the manner of jet generation will be affected by the phase difference between bubbles. With the increasing of phase difference, the directive property of noise becomes obvious. With the enlargement of initial inner pressure, the sound pressure will arise at the early stage of expanding, and the increasing of buoyance parameter will reduce the sound pressure after the generation of jet. Since the consideration of compressibility, the oscillation amplitude of bubbles will be weakened. Originality/value – The paper could provide the reference for the research about the dynamics and noise characteristics of multiple bubbles in compressible fluid. And the new method based on boundary integral equation to simulate the multiple bubbles motion and noise radiation is presented.

PurposeThis paper aims to calculate the mixed‐mode stress intensity factors (SIFs) of a 3D crack meeting the interface in a bimaterial under shear loading by a hypersingular integral equation (HIE) method, And further to assess the accuracy of numerical solutions for the mixed mode SIFs along the crack front.Design/methodology/approachA 3D crack modeling is reduced to solving a set of HIEs. Based on the analytical solutions of the singular stress field around the crack front, a numerical method for the HIEs is proposed by a finite‐part integral method, where the displacement discontinuities of the crack surface are approximated by the product of basic density functions and polynomials. Using FORTRAN program, numerical solutions of the mixed‐mode SIFs of some examples are presented.FindingsThe numerical method is proved to be an effective construction technique. The numerical results show that this numerical technique is successful, and the solution precision is satisfied.Research limitations/implicationsThis work takes further steps to improve the fundamental systems of HIE for its application in the fields of arbitrary shape crack problems. Propose several techniques for numerical implementation, which could increase the efficiency and accuracy of computation.Practical implicationsWhenever there is a structure containing the 3D crack, the analysis method described in this paper can be utilized to find the critical configurations under which the structure may be most vulnerable. In such cases, the strength predictions would be safer if the crack could be taken into account.Originality/valueThis paper is the first to apply HIE method to analyzing the mixed‐mode crack meeting the interface in 3D dissimilar materials. Numerical solutions of the mixed‐mode SIFs can give the satisfied solution precision.

PurposeThis paper aims to develop an integrated cooling simulation for the temperature history of the panel during the forming process.Design/methodology/approachA local one‐dimensional transient analysis in the thickness direction is adopted for the panel part, which employs finite‐difference method. And a three‐dimensional, boundary element method is used for the numerical implementation of the heat transfer analysis in the mold region, which is considered as three‐dimensional conduction. The Renormalization‐Group turbulence model is applied for the jet impinging cooling. The part and mold analyses are coupled so as to match the temperature and heat flux on the glass‐mold interface.FindingsThe paper provides mathematical model and numerical strategy adapted to the problem, with experimental verification that shows a good agreement.Practical implicationsCooling design in the forming operation of picture tube panel is of great importance because it significantly affects the part quality associated with residual stresses and productivity. The developed simulation package is a tool in the optimization of processing parameters and in‐mold cooling system structure design.Originality/valueThis paper presents a realistic, integrated, and coupled numerical model for analyzing the panel cooling process that retains important aspects of the problem. The paper could be very valuable to the researchers in this field as a benchmark for their analyses.

PurposeThis paper describes an approach for the automatic calculation of view factors between surfaces of arbitrary shape, when taking into account possible screening effects due to intermediate surfaces.Design/methodology/approachThe specifically developed numerical code is based on the utilization of boundary elements to fit the surfaces of an algorithm solving the shadow effect and on a Monte Carlo method for the numerical integrations.FindingsThe code has been tested for a set of geometrical configurations. It was clearly shown that it obtains good results in terms of accuracy and computing time. Its accuracy increases when the mesh of radiative surfaces is finer.Research limitations/implicationsThe use of the code is limited to opaque surfaces separated by an isothermal semi‐transparent medium which can be absorbent but not diffusing of the thermal radiation.Practical implicationsThe study of the radiative exchanges between opaque surfaces with shadow effects due to intermediate surfaces may have concrete practical applications by using this code. Indeed, the code has been used for an industrial application, in order to evaluate view factors inside an enclosure, in the framework of studies concerned with the thermal comfort inside cars.Originality/valueThe originality of this paper lies in taking into account the surfaces of complex geometries by using a boundary elements approximation, the algorithm solving the shadow effect, based on the convexity of the quadrilateral in 2D or the polyhedron in 3D.

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.

An efficient boundary element method (BEM) formulation for three‐dimensional elastoplasticity is presented in this paper. The BEM formulation for nonlinear problems requires discretization of the surface as well as part of the volume. In this paper nine‐noded quadrilateral elements are used for modelling the surface and 27‐noded brick elements for the volume. Particular attention is paid to the accurate evaluation of the Cauchy principal value volume integrals appearing in the interior stress calculations. An explicit initial strain formulation is used to satisfy the non‐linearity. The accuracy of the proposed method is demonstrated by solving a number of benchmark problems.

PurposeThe purpose of this paper is to revisit the recursive computation of closed-form expressions for the topological derivative of shape functionals in the context of time-harmonic acoustic waves scattering by sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions).Design/methodology/approachThe elliptic boundary value problems in the singularly perturbed domains are equivalently reduced to couples of boundary integral equations with unknown densities given by boundary traces. In the case of circular or spherical holes, the spectral Fourier and Mie series expansions of the potential operators are used to derive the first-order term in the asymptotic expansion of the boundary traces for the solution to the two- and three-dimensional perturbed problems.FindingsAs the shape gradients of shape functionals are expressed in terms of boundary integrals involving the boundary traces of the state and the associated adjoint field, then the topological gradient formulae follow readily.Originality/valueThe authors exhibit singular perturbation asymptotics that can be reused in the derivation of the topological gradient function in the iterated numerical solution of any shape optimization or imaging problem relying on time-harmonic acoustic waves propagation. When coupled with converging Gauss−Newton iterations for the search of optimal boundary parametrizations, it generates fully automatic algorithms.

This bibliography is offered as a practical guide to published papers, conference proceedings papers and theses/dissertations on the finite element (FE) and boundary element (BE) applications in different fields of biomechanics between 1976 and 1991. The aim of this paper is to help the users of FE and BE techniques to get better value from a large collection of papers on the subjects. Categories in biomechanics included in this survey are: orthopaedic mechanics, dental mechanics, cardiovascular mechanics, soft tissue mechanics, biological flow, impact injury, and other fields of applications. More than 900 references are listed.

Purpose The purpose of this paper is to present an accurate and efficient element for analysis of spherical shell structures. Design/methodology/approach A scaled boundary finite element method is proposed, which offers more advantages than the finite element method and boundary element method. Only the boundary of the computational domain needs to be discretized, but no fundamental solution is required. Findings The method applies to thin as well as thick spherical shells, irrespective of the shell geometry, boundary conditions and applied loading. The numerical solution converges to highly accurate result with raising the order of high-order elements. Originality/value The modeling strictly follows three-dimensional theory of elasticity. Formulation of the surface finite elements using three translational degree of freedoms per node is required, which results in considerably simplifying the computation. In the thickness directions, it is solved analytically, no problem of high aspect ratio arises and transverse shear locking can be successfully avoided.

Purpose This paper aims to develop a new isogeometric boundary element formulation based on non-uniform rational basis splines (NURBS) curves for solving Reissner’s shear-deformable plates. Design/methodology/approach The generalized displacements and tractions along the problem boundary are approximated as NURBS curves having the same rational B-spline basis functions used to describe the geometrical boundary of the problem. The source points positions are determined over the problem boundary by the well-known Greville abscissae definition. The singular integrals are accurately evaluated using the singularity subtraction technique. Findings Numerical examples are solved to demonstrate the validity and the accuracy of the developed formulation. Originality/value This formulation is considered to preserve the exact geometry of the problem and to reduce or cancel mesh generation time by using NURBS curves employed in computer aided designs as a tool for isogeometric analysis. The present formulation extends such curves to be implemented as a stress analysis tool.

Purpose The purpose of this paper is to evaluate the efficiency of the fast multipole boundary element method (FMBEM) in the analysis of stress and effective properties of 3D linear elastic structures with cavities. In particular, a comparison between the FMBEM and the finite element method (FEM) is performed in terms of accuracy, model size and computation time. Design/methodology/approach The developed FMBEM uses eight-node Serendipity boundary elements with numerical integration based on the adaptive subdivision of elements. Multipole and local expansions and translations involve solid harmonics. The proposed model is used to analyse a solid body with two interacting spherical cavities, and to predict the homogenized response of a porous material under linear displacement boundary condition. The FEM results are generated in commercial codes Ansys and MSC Patran/Nastran, and the results are compared in terms of accuracy, model size and execution time. Analytical solutions available in the literature are also considered. Findings FMBEM and FEM approximate the geometry with similar accuracy and provide similar results. However, FMBEM requires a model size that is smaller by an order of magnitude in terms of the number of degrees of freedom. The problems under consideration can be solved by using FMBEM within the time comparable to the FEM with an iterative solver. Research limitations/implications The present results are limited to linear elasticity. Originality/value This work is a step towards a comprehensive efficiency evaluation of the FMBEM applied to selected problems of micromechanics, by comparison with the commercial FEM codes.

Purpose The purpose of this paper is to preset a spherical element subdivision method for the numerical evaluation of nearly singular integrals in three-dimensional (3D) boundary element method (BEM). Design/methodology/approach In this method, the source point is first projected to the tangent plane of the element. Then two cases are considered: the projection point is either inside or outside the element. In both cases, the element is subdivided into a number of patches using a sequence of spheres with decreasing radius. Findings With the proposed method, the patches obtained are automatically refined as they approach the projection point and each patch of the integration element is “good” in shape and size for standard Gaussian quadrature. Therefore, all kinds of nearly singular boundary integrals on elements of any shape and size with arbitrary source point location related to the element can be evaluated accurately and efficiently. Originality/value Numerical examples for planar and slender elements with various relative location of the source point are presented. The results demonstrate that our method has much better accuracy, efficiency and stability than conventional methods.

Purpose Domain integrals, known as volume potentials in 3D elasticity problems, exist in many boundary-type methods, such as the boundary element method (BEM) for inhomogeneous partial differential equations. The purpose of this paper is to develop an accurate and reliable technique to effectively evaluate the volume potentials in 3D elasticity problems. Design/methodology/approach An adaptive background cell-based domain integration method is proposed for treatment of volume potentials in 3D elasticity problems. The background cells are constructed from the information of the boundary elements based on an oct-tree structure, and the domain integrals are evaluated over the cells rather than volume elements. The cells that contain the boundary elements can be subdivided into smaller sub-cells adaptively according to the sizes and levels of the boundary elements. The fast multipole method (FMM) is further applied in the proposed method to reduce the time complexity of large-scale computation. Findings The method is a boundary-only discretization method, and it can be applied in the BEM easily. Much computational time is saved by coupling with the FMM. Numerical examples demonstrate the accuracy and efficiency of the proposed method.. Originality/value Boundary elements are used to create adaptive background cells, and domain integrals are evaluated over the cells rather than volume elements. Large-scale computation is made possible by coupling with the FMM.

Purpose The purpose of this paper is to detect the degenerate scale of a 2D bending plate analytically and numerically. Design/methodology/approach To avoid the time-consuming scheme, the influence matrix of the boundary element method (BEM) is reformulated to an eigenproblem of the 4 by 4 matrix by using the scaling transform instead of the direct-searching scheme to find degenerate scales. Analytical degenerate scales are derived from the boundary integral equation (BIE) by using the degenerate kernel only for the circular case. Numerical results of the direct-searching scheme and the eigen system for the arbitrary shape are also considered. Findings Results using three methods, namely, analytical derivation, the direct-searching scheme and the 4 by 4 eigen system, are also given for the circular case and arbitrary shapes. Finally, addition of a constant for the kernel function makes original eigenvalues (2 real roots and 2 complex roots) of the 4 by 4 matrix to be all real. This indicates that a degenerate scale depends on the kernel function. Originality/value The analytical derivation for the degenerate scale of a 2D bending plate in the BIE is first studied by using the degenerate kernel. Through the reformed eigenproblem of a 4 by 4 matrix, the numerical solution for the plate of an arbitrary shape can be used in the plate analysis using the BEM.

Purpose The purpose of this paper is to extend the meshless local exponential basis functions (MLEBF) method to the case of nonlinear and linear, variable coefficient partial differential equations (PDEs). Design/methodology/approach The original version of MLEBF method is limited to linear, constant coefficient PDEs. The reason is that exponential bases which satisfy the homogeneous operator can only be determined for this class of problems. To extend this method to the general case of linear PDEs, the variable coefficients along with all involved derivatives are first expanded. This expanded form is evaluated at the center of each cloud, and is assumed to be constant over the entire cloud. The solution procedure is followed as in the former version. Nonlinear problems are first converted to a succession of linear, variable coefficient PDEs using the Newton-Kantorovich scheme and are subsequently solved using the aforementioned approach until convergence is achieved. Findings The results obtained show good performance of the method as solution to a wide range of problems. The results are compared with the well-known methods in the literature such as the finite element method, high-order finite difference method or variants of the boundary element method. Originality/value The MLEBF method is a simple yet effective tool for analyzing various kinds of problems. It is easy to implement with high parallelization potential. The proposed method addresses the biggest limitation of the method, and extends it to linear, variable coefficient PDEs as well as nonlinear ones.

Purpose – The purpose of this paper is to develop an easy-to-implement and accurate fast boundary element method (BEM) for solving large-scale elastodynamic problems in frequency and time domains. Design/methodology/approach – A newly developed kernel-independent fast multipole method (KIFMM) is applied to accelerating the evaluation of displacements, strains and stresses in frequency domain elastodynamic BEM analysis, in which the far-field interactions are evaluated efficiently utilizing equivalent densities and check potentials. Although there are six boundary integrals with unique kernel functions, by using the elastic theory, the authors managed to accelerate these six boundary integrals by KIFMM with the same kind of equivalent densities and check potentials. The boundary integral equations are discretized by Nyström method with curved quadratic elements. The method is further used to conduct the time-domain analysis by using the frequency-domain approach. Findings – Numerical results show that by the fast BEM, high accuracy can be achieved and the computational complexity is brought down to linear. The performance of the present method is further demonstrated by large-scale simulations with more than two millions of unknowns in the frequency domain and one million of unknowns in the time domain. Besides, the method is applied to the topological derivatives for solving elastodynamic inverse problems. Originality/value – An efficient KIFMM is implemented in the acceleration of the elastodynamic BEM. Combining with the Nyström discretization based on quadratic elements and the frequency-domain approach, an accurate and highly efficient fast BEM is achieved for large-scale elastodynamic frequency domain analysis and time-domain analysis.

PurposeThis paper computationally estimates the constitutive relationships of composite materials reinforced by single walled carbon nanotubes (SWNT).Design/methodology/approachA multiscale analysis is considered. At the nanoscale level, molecular dynamics (MD) are used to predict the stiffness for an equivalent beam. A BEM solver for the elasticity problems is extended to allow the presence of inclusions and hence is used to model a RVE for the composite matrix with the equivalent nanotube beams. A genetic algorithm (GA) is developed to generate an initial population of anisotropic materials based on FEM. The GA evolves the population of properties of anisotropic materials till a material is found whose mechanical response is the same as that of the nanocomposite.FindingsThe overall process is suitable for the constitutive relationships estimation according to the verification process outlined.Research limitations/implicationsThe present work is limited to 2D linear problems. However, extending it to 3D non‐linear applications is straight forward.Practical implicationsThe present technique could be used to estimate properties of NCT composites, hence practical applications such as aeroplane structures or turbine blades could be analysed using commercial finite element software. The present methodology could be used to estimate non‐mechanical properties such as the thermal and electric properties.Originality/valueThe present computational technique has never been presented in the literature.

PurposeThe purpose of this paper is to present special nine‐node quadrilateral elements to discretize the un‐cracked boundary and the inclined surface crack in a transversely isotropic cuboid under a uniform vertical traction along its top and bottom surfaces by a three‐dimensional (3D) boundary element method (BEM) formulation. The mixed‐mode stress intensity factors (SIFs), KI, KII and KIII, are calculated.Design/methodology/approachA 3D dual‐BEM or single‐domain BEM is employed to solve the fracture problems in a linear anisotropic elastic cuboid. The transversely isotropic plane has an arbitrary orientation, and the crack surface is along an inclined plane. The mixed 3D SIFs are evaluated by using the asymptotical relation between the SIFs and the relative crack opening displacements.FindingsNumerical results show clearly the influence of the material and crack orientations on the mixed‐mode SIFs. For comparison, the mode‐I SIF when a horizontal rectangular crack is embedded entirely within the cuboid is calculated also. It is observed that the SIF values along the crack front are larger when the crack is closer to the surface of the cuboid than those when the crack is far away from the surface.Research limitations/implicationsThe FORTRAN program developed is limited to regular surface cracks which can be discretized by the quadrilateral shape function; it is not very efficient and suitable for irregular crack shapes.Practical implicationsThe evaluation of the 3D mixed‐mode SIFs in the transversely isotropic material may have direct practical applications. The SIFs have been used in engineering design to obtain the safety factor of the elastic structures.Originality/valueThis is the first time that the special nine‐node quadrilateral shape function has been applied to the boundary containing the crack mouth. The numerical method developed can be applied to the SIF calculation in a finite transversely isotropic cuboid within an inclined surface crack. The computational approach and the results of SIFs are of great value for the modeling and design of anisotropic elastic structures.

PurposeThe purpose of this paper is to introduce a novel approach to solving linear systems arising from applying a Boundary Element Method (BEM) to elasticity problems.Design/methodology/approachThe key idea is based on using wavelet transforms as a tool to change dense and fully populated matrices of BEM systems into sparse matrices. Wavelets are then used again to produce an algorithm to solve the resultant sparse linear systems. The wavelet transformation part of the method can be added as a black box to existing BEM codes.FindingsNumerical results focusing on the sensitivity of the solution for various physical variables to the thresholding parameters, and savings in computer time and memory are presented. The results show that the proposed method is efficient for large problems.Research limitations/implicationsApplication of the proposed method is restricted to problems with number of DOF equal to an integer power of 2.Originality/valueThe novel algorithm to solve transformed algebraic linear equations uses NS‐form of the modified matrix, taking the advantage of the hierarchical nature of Multi‐Resolution Analysis (MRA) to decompose a parent system into descendant systems with reduced size. These smaller systems are then solved iteratively using generalized minimal residual method.

This paper aims to calculate the mixed-mode stress intensity factors (SIFs) of a three-dimensional crack meeting the interface in a bimaterial under shear loading by a hypersingular integral equation (HIE) method, And further to assess the accuracy of numerical solutions for the mixed mode SIFs along the crack front.

PurposeIn the finite element analysis of a hot forging process, it is difficult to design an optimal preform because of highly nonlinear characteristics of design variables. In this paper, a new preform design method which can reduce the forming load and the die wear by removing the flash is developed and applied to the pre form design of a piston.Design/methodology/approachAfter finite element analyses of hot forging processes, if the final product is found to have excessive flash and cause high die wear, a new preform design technique, so‐called iterative preform design technique is applied to obtain an optimal preform design. From the results of FE simulations, a boundary region at the outlet of the flash is first selected. Then, by tracing the section along the deformation path to the initial billet, it is possible to obtain a mapped section boundary in the initial billet. After updating the initial shape by removing the exterior region of the mapped section boundary, a finite element simulation is carried out with the updated initial shape. Iterations should be continued until a desired result is obtained.FindingsIt has been confirmed that the proposed preform design technique has a negligible effect on the initial forgeability of the workpiece. It is expected that the tool life will be increased, because the forming load and die wear are reduced as the number of iterations are increased. Moreover, because the preform design reduces the flash, it thereby reduces the waste of material.Originality/valueIn the 3D finite element analysis of a hot forging process, several optimal preform design techniques have been developed. However, it is difficult to use the techniques in general problems because it is difficult to formulate cost functions, which mainly depend on the experience and physical insight of the designer. In addition, tremendous time is consumed in optimizing a problem as a large number of iterations are required in minimizing the objective function. The proposed preform design technique is simple enough to apply to general hot forging problems involving excessive flash. The proposed preform design technique is an offline method and easy to apply to any other analysis program, including commercial programs.

PurposeTo present numerical approaches to the solution of physically coupled non‐linear problems, which frequently happen to be characterized by their multi‐domain character.Design/methodology/approachBy adopting coupled solution strategies a considerable attention is devoted, in order to obtain a computationally efficient numerical algorithm, to the selection of appropriate space and time discretization, as well as to a proper discrete approximation method used.FindingsCoupling of two methods, the finite element method and the boundary element method, respectively, has proved to be computationally exceedingly advantageous, particularly in case of moving domains.Practical implicationsAs specific case studies computer simulation of an induction heating problem and a mushy‐state forming problem are considered. A thorough discussion on the coupling effects, characterizing the evolutions of respective physical quantities' fields, is given, and their impact on those evolutions is identified.Originality/valueThis paper presents efficient numerical strategies for the solution of a certain class of multi‐physics and multi‐domain problems.

An indirect symmetric Galerkin BEM (SGBEM) is applied to 2D potential problems in this paper. Based on the assumption that solutions from different methods should be the same, the hypersingular matrix appeared in SGBEM is approximately expressed by those matrices appeared in asymmetric Galerkin BEM (AGBEM). As only strong and weak singularities need to be solved, the problem becomes much simpler. The space derivatives of potential are expressed with a set of new meaning distributed flux, which will produce the same potential on the boundary position for Ω in the unbounded domain Ω+Ω′, so that hypersingularity will not appear for boundary points. Therefore, there is no need of C1,α for the spatial interpolation function (no Galerkin integration can be used for this purpose). Formulations for both the steady‐state and time‐domain potential problems are given. Three numerical examples are analyzed to demonstrate the effectiveness and accuracy of the proposed indirect method.

In this paper, an interpolation method called the quasi‐higher order element method (QHOEM) is proposed for solving elastoplastic problems using symmetric Galerkin boundary element method (SGBEM). At the initial stage, it uses higher order elements to interpolate the coordinates and the field variables. Then, for the numerical integration involved, it further uses interpolation to decompose the higher order elements into lower order elements so that the existing analytical integration formulas can be applied. By adopting this procedure, the proposed method yields good adaptability and reduces the computational cost. Its accuracy and efficiency are demonstrated by analyzing three practical examples.