Paras Ram¹, Anupam Bhandari²

FDMP-Fluid Dynamics & Materials Processing, Vol.8, No.4, pp. 437-452, 2012, DOI:10.3970/fdmp.2012.008.437

Abstract The present problem is formulated by considering the dynamics of a ferromagnetic fluid of variable viscosity permeating a porous medium in a rotating system in the presence of a stationary boundary. The fluid at large distance from such a boundary (disk) is assumed to rotate at a given uniform angular velocity. The viscosity of the fluid is assumed to depend on the intensity of the applied magnetic field. The governing nonlinear partial differential equations are transformed into a set of coupled nonlinear ordinary differential equations resorting to a similarity transformation. The resulting system of equations is solved numerically by applying… More >

L. Godinho A. ¹, A. Tadeu¹, P. Amado Mendes¹

CMC-Computers, Materials & Continua, Vol.5, No.2, pp. 117-128, 2007, DOI:10.3970/cmc.2007.005.117

Abstract This paper presents a strategy for using the Method of Fundamental Solutions (MFS) to model the propagation of elastic waves around thin structures, like empty cracks or thin rigid screens, located in a homogeneous elastic medium. The authors make use of a simple approach for modeling these propagation conditions using the MFS together with decomposition of the domain into distinct regions. This approach makes it possible to avoid the undetermined system of equations that arises from imposing boundary conditions at both sides of a thin structure. The numerical implementation of the MFS is performed in the frequency domain, making use… More >

Kang Qiong^1,*, Xinting Li²

CMC-Computers, Materials & Continua, Vol.58, No.1, pp. 121-133, 2019, DOI:10.32604/cmc.2019.03723

Abstract The introduction of graph-theoretical structure descriptors represents an important step forward in the research of predictive models in chemistry and falls within the lines of the increasing use of mathematical and computational methods in contemporary chemistry. The basis for these models is the study of the quantitative structure-property and structure-activity relationship. In this paper, we investigate Great rhom-bitrihexagonal which is a kind of dodecagon honeycomb net-work covered by quadrangle and hexagon. Many topological indexes of Great rhom-bitrihexagonal have being investigated, such as sum-connectivity index, atom-bond connectivity index, geometric-arithmetic index, fifth, harmonic index, Randić connectivity index, first Zagreb index, second Zagreb… More >

P.G. Santos¹, J. Carbajo², L. Godinho³, J. Ramis²

CMC-Computers, Materials & Continua, Vol.43, No.2, pp. 109-136, 2014, DOI:10.3970/cmc.2014.043.109

Abstract The study of periodic structures, namely sonic crystals, for sound attenuation purposes has been a topic of intense research in the last years. Some efficient methods are available in literature to solve the problem of sound propagation in the presence of this kind of structures such as those based in the Multiple Scattering Theory (MST) or the Finite Element Method (FEM). In this paper a solution based on the Method of Fundamental Solutions (MFS) which presents advantages, namely in computational discretization and calculation costs, is presented. The proposed formulation considers the presence of elastic ring shaped scatterers, correctly accounting for… More >

Liviu Marin¹

CMC-Computers, Materials & Continua, Vol.17, No.3, pp. 233-274, 2010, DOI:10.3970/cmc.2010.017.233

Abstract We investigate two algorithms involving the relaxation of either the given boundary temperatures (Dirichlet data) or the prescribed normal heat fluxes (Neumann data) on the over-specified boundary in the case of the iterative algorithm of Kozlov91 applied to Cauchy problems for two-dimensional steady-state anisotropic heat conduction (the Laplace-Beltrami equation). The two mixed, well-posed and direct problems corresponding to every iteration of the numerical procedure are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV)… More >

LiviuMarin ¹

CMC-Computers, Materials & Continua, Vol.12, No.1, pp. 71-100, 2009, DOI:10.3970/cmc.2009.012.071

Abstract In this paper, the alternating iterative algorithm originally proposed by Kozlov, Maz'ya and Fomin (1991) is numerically implemented for the Cauchy problem in anisotropic heat conduction using a meshless method. Every iteration of the numerical procedure consists of two mixed, well-posed and direct problems which are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise… More >

Liviu Marin¹, Andreas Karageorghis²

CMC-Computers, Materials & Continua, Vol.10, No.3, pp. 259-294, 2009, DOI:10.3970/cmc.2009.010.259

Abstract We study the stable numerical identification of an unknown portion of the boundary on which a given boundary condition is provided and additional Cauchy data are given on the remaining known portion of the boundary of a two-dimensional domain for problems governed by either the Helmholtz or the modified Helmholtz equation. This inverse geometric problem is solved using the method of fundamental solutions (MFS) in conjunction with the Tikhonov regularization method. The optimal value for the regularization parameter is chosen according to Hansen's L-curve criterion. The stability, convergence, accuracy and efficiency of the proposed method are investigated by considering several… More >

T. Tsangaris¹, Y.–S. Smyrlis^{1, 2}, A. Karageorghis^{1, 2}

CMC-Computers, Materials & Continua, Vol.1, No.3, pp. 245-258, 2004, DOI:10.3970/cmc.2004.001.245

Abstract The Method of Fundamental Solutions (MFS) is a boundary-type method for the solution of certain elliptic boundary value problems. In this work, we develop an efficient matrix decomposition MFS algorithm for the solution of biharmonic problems in annular domains. The circulant structure of the matrices involved in the MFS discretization is exploited by using Fast Fourier Transforms. The algorithm is tested numerically on several examples. More >