Chein-Shan Liu¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 57-68, 2007, DOI:10.3970/icces.2007.003.057

Abstract A new method is developed to solve the interior and exterior Dirichlet problems for the two-dimensional Laplace equation, namely the meshless regularized integral equation method (MRIEM), which consists of three parts: Fourier series expansion, the second kind Fredholm integral equation and an analytically regularized solution of the unknown boundary condition on an artificial circle. We find that the new method is powerful even for the problem with very complex boundary shape and with boundary noise. More >

Godwin Kakuba^1,∗, John M. Mango¹, Martijn J.H. Anthonissen²

CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 207-225, 2019, DOI:10.32604/cmes.2019.04269

Abstract Sometimes boundary value problems have isolated regions where the solution changes rapidly. Therefore, when solving numerically, one needs a fine grid to capture the high activity. The fine grid can be implemented as a composite coarse-fine grid or as a global fine grid. One cheaper way of obtaining the composite grid solution is the use of the local defect correction technique. The technique is an algorithm that combines a global coarse grid solution and a local fine grid solution in an iterative way to estimate the solution on the corresponding composite grid. The algorithm is relatively new and its convergence… More >

B. Chandrasekhar¹

CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.3, pp. 243-254, 2005, DOI:10.3970/cmes.2005.009.243

Abstract In this work, a novel numerical technique is presented to calculate the acoustic fields scattered by three dimensional rigid bodies of arbitrary shape using the method of moment's solution procedure. A new set of basis functions, namely, Node based basis functions are developed to represent the source distribution on the surface of rigid body and the same functions are used as testing functions as well. Both single layer formulation and double layer formulations are numerically solved using the same basis functions. The surface of the body is modeled by triangular patch modeling. Numerical technique presented in this paper, using these… More >

J. Purbolaksono¹, M. H. Aliabadi^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.1, pp. 73-90, 2005, DOI:10.3970/cmes.2005.008.073

Abstract This paper presents the dual boundary integral equations for the buckling analysis of the shear deformable cracked plates. The domain integrals which appear in this formulation are transferred to boundary integrals using the dual reciprocity method. The plate buckling displacement and hypersingular traction integral equations are presented as a standard eigenvalue problem, which would allow direct evaluation of the critical load factor and buckling modes. Several examples with different geometries and boundary conditions are presented to demonstrate the accuracy of the proposed formulation. More >

Zai You Yan^1,2, Fang Sen Cui², Kin Chew Hung²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.1, pp. 97-106, 2005, DOI:10.3970/cmes.2005.007.097

Abstract Taking the normal derivative of solid angles on the surface into account, a modified Burton and Miller's formulation is derived. From which, a more reasonable expression of the hypersingular operator is obtained. To overcome the hypersingular integral, the regularization scheme developed recently is employed. Plane acoustic wave scattering from a rigid sphere is computed to show the correctness of the modified formulation with the regularization scheme. In the computation, eight-nodded isoparametric element is applied. More >

V. Sladek¹, J. Sladek¹, M. Tanaka²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.1, pp. 69-84, 2005, DOI:10.3970/cmes.2005.007.069

Abstract An efficient numerical method is proposed for 2-d potential problems in anisotropic media with continuously variable material coefficients. The method is based on the local integral equations (utilizing a fundamental solution) and meshfree approximation of field variable. A lot of numerical experiments are carried out in order to study the numerical stability, accuracy, convergence and efficiency of several approaches utilizing various interpolations. More >

E. J. Sellountos¹, V. Vavourakis², D. Polyzos³

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.1, pp. 35-48, 2005, DOI:10.3970/cmes.2005.007.035

Abstract A new meshless local Petrov-Galerkin (MLPG) type method based on local boundary integral equation (LBIE) considerations is proposed for the solution of elastostatic problems. It is called singular/hypersingular MLPG (LBIE) method since the representation of the displacement field at the internal points of the considered structure is accomplished with the aid of the displacement local boundary integral equation, while for the boundary nodes both the displacement and the corresponding traction local boundary integral equations are employed. Nodal points spread over the analyzed domain are considered and the moving least squares (MLS) interpolation scheme for the approximation of the interior and… More >

Z. D. Han¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.2, pp. 169-188, 2004, DOI:10.3970/cmes.2004.006.169

Abstract Three different truly Meshless Local Petrov-Galerkin (MLPG) methods are developed for solving 3D elasto-static problems. Using the general MLPG concept, these methods are derived through the local weak forms of the equilibrium equations, by using different test functions, namely, the Heaviside function, the Dirac delta function, and the fundamental solutions. The one with the use of the fundamental solutions is based on the local unsymmetric weak form (LUSWF), which is equivalent to the local boundary integral equations (LBIE) of the elasto-statics. Simple formulations are derived for the LBIEs in which only weakly-singular integrals are included for a simple numerical implementation.… More >

Z.Y. Qian¹, Z.D. Han¹, P. Ufimtsev¹, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.2, pp. 133-144, 2004, DOI:10.3970/cmes.2004.006.133

Abstract The weak-form of Helmholtz differential equation, in conjunction with vector test-functions (which are gradients of the fundamental solutions to the Helmholtz differential equation in free space) is utilized as the basis in order to directly derive non-hyper-singular boundary integral equations for the velocity potential, as well as its gradients. Thereby, the presently proposed boundary integral equations, for the gradients of the acoustic velocity potential, involve only O(r⁻²) singularities at the surface of a 3-D body. Several basic identities governing the fundamental solution to the Helmholtz differential equation for velocity potential, are also derived for the further desingularization of the strongly… More >

Z.Y. Qian¹, Z.D. Han¹, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.1, pp. 115-122, 2004, DOI:10.3970/cmes.2004.006.115

Abstract This article has no abstract. More >