Jun-Sheng Duan¹, Ai-Ping Guo²

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.2, pp. 139-150, 2010, DOI:10.3970/cmes.2010.060.139

Abstract Adomian polynomials are constituted of reduced polynomials and derivatives of nonlinear operator. The reduced polynomials are independent of the form of the nonlinear operator. A recursive algorithm of the reduced polynomials is discovered and its symbolic implementation by the software Mathematica is given. As a result, a new and convenient algorithm for the Adomian polynomials is obtained. More >

Chia-Cheng Tsai¹

CMES-Computer Modeling in Engineering & Sciences, Vol.45, No.3, pp. 249-272, 2009, DOI:10.3970/cmes.2009.045.249

Abstract Analytical particular solutions of Chebyshev polynomials are obtained for problems of Reissner plates under arbitrary loadings, which are governed by three coupled second-ordered partial differential equation (PDEs). Our solutions can be written explicitly in terms of monomials. By using these formulas, we can obtain the approximate particular solution when the arbitrary loadings have been represented by a truncated series of Chebyshev polynomials. In the derivations of particular solutions, the three coupled second-ordered PDE are first transformed into a single six-ordered PDE through the Hörmander operator decomposition technique. Then the particular solutions of this six-ordered PDE can be found in the… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.1, pp. 25-38, 2008, DOI:10.3970/cmes.2008.038.025

Abstract In this paper a complex matrix operator and a complex field are used to express the Maxwell equations, of which the complex field embraces all field variables and the matrix operator embraces the time and space differential operators. By left applying the operator on the complex field one can get all the four Maxwell equations, which are usually expressed by the vector form. The new formulation matches the Lorenz gauge condition, and its mathematical advantage is that it can incorporate the Maxwell equations into a single equation. The introduction of four-potential is possible only under the Lorenz gauge. In terms… More >

Yoshitaka Suetake¹, Masashi Iura², S. N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 329-336, 2003, DOI:10.3970/cmes.2003.004.329

Abstract The objective of this paper is to examine the symmetry of the tangent operator for nonlinear shell theories with the finite rotation field. As well known, it has been stated that since the rotation field carries the Lie group structure, not a vector space one, the tangent operator incorporating the rotation field does not become symmetric. In this paper, however, it is shown that by adopting a rotation vector as a variable, the symmetry can be achieved in the Lagrangean (material) description. First, we present a general concept for the problem. Next, we adopt the finitely deformed thick shell problem… More >

R.Kanapady¹, K.K.Tamma²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 103-118, 2003, DOI:10.3970/cmes.2003.004.103

Abstract Of general interest here is the time dimension aspect wherein discretized operators in time may be continuous or discontinuous; and of particular interest and focus here is the design of time discretized operators in the context of discontinuous state-phase for computational dynamics applications. Based on a generalized bi-discontinuous time weighted residual formulation, the design leading to a new unified set of hierarchical energy conserving and energy dissipating time discretized operators are developed for the first time that are fundamentally useful for time adaptive computations for dynamic problems. Unlike time discontinuous Galerkin approaches, the design is based upon a time discontinuous… More >

D. Boffi¹, C. Chinosi², L. Gastaldi³

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 31-44, 2000, DOI:10.3970/cmes.2000.001.191

Abstract In this paper we are dealing with the approximation of the grad-div operator in nonconvex polygonal domains. A penalization strategy is considered in order to obtain a formulation of the original eigenproblem which is associated with an elliptic operator. However the presence of singular eigensolutions, in the case of nonconvex domains, is the origin of major troubles in the numerical approximation of the problem. A mixed-type approximation, based on a projection procedure, is introduced and analyzed from the theoretical and numerical point of view. Several numerical experiments confirm that in presence of singularities the projection is needed in order to… More >

Anand L. Pardhanani¹, Graham F. Carey¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.1, pp. 141-150, 2000, DOI:10.3970/cmes.2000.001.141

Abstract Rapid prototyping tools that combine powerful numerics with a flexible applications interface can play a significant role in micro-scale modeling and simulation. We demonstrate this idea using the PROPHET simulator. In the first part of the investigations we extend the simulator's capability to allow analysis of carrier transport in deep submicron MOSFETs using a hydrodynamic model. The model is numerically implemented within PROPHET's dial-an-operator framework by adding certain "flux'' routines. Once implemented, the model becomes available for use in any number of spatial dimensions. We present results for MOSFET type test problems in one and two dimensions. The second application… More >

S.D. Akbarov^1,2, M. Negin³

CMC-Computers, Materials & Continua, Vol.53, No.4, pp. 307-341, 2017, DOI:10.3970/cmc.2017.053.307

Abstract Dispersion of the generalized Rayleigh waves propagating in a covered half-space made of viscoelastic materials is investigated by utilizing the exact equations of the theory of linear viscoelasticity. The dispersion equation is obtained for an arbitrary type of hereditary operator of the materials of the constituents and a solution algorithm is developed for obtaining numerical results on the dispersion of the waves under consideration. Dispersion curves are presented for certain attenuation cases and the influence of the viscosity of the materials is studied through three rheological parameters of the viscoelastic materials which characterize the characteristic creep time, long-term values and… More >