Bart Bergen¹, Bert Van Genechten¹, Dirk Vandepitte¹, Wim Desmet¹

CMES-Computer Modeling in Engineering & Sciences, Vol.61, No.2, pp. 155-176, 2010, DOI:10.3970/cmes.2010.061.155

Abstract The Wave Based Method (WBM) is a numerical prediction technique for Helmholtz problems. It is an indirect Trefftz method using wave functions, which satisfy the Helmholtz equation, for the description of the dynamic variables. In this way, it avoids both the large systems and the pollution errors that jeopardize accurate element-based predictions in the mid-frequency range. The enhanced computational efficiency of the WBM as compared to the element-based methods has been proven for the analysis of both three-dimensional bounded and two-dimensional unbounded problems. This paper presents an extension of the WBM to the application of three-dimensional acoustic scattering and radiation… More >

M. R. Swager¹, L. J. Gray², S. Nintcheu Fata²

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.3, pp. 297-312, 2010, DOI:10.3970/cmes.2010.058.297

Abstract A linear element Galerkin boundary integral analysis for the three-dimensional Helmholtz equation is presented. The emphasis is on solving acoustic scattering by an open (crack) surface, and to this end both a dual equation formulation and a symmetric hypersingular formulation have been developed. All singular integrals are defined and evaluated via a boundary limit process, facilitating the evaluation of the (finite) hypersingular Galerkin integral. This limit process is also the basis for the algorithm for post-processing of the surface gradient. The analytic integrations required by the limit process are carried out by employing a Taylor series expansion for the exponential… More >

A. Frangi¹, M. Bonnet²

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.3, pp. 271-296, 2010, DOI:10.3970/cmes.2010.058.271

Abstract This paper presents an empirical study of the accuracy of multipole expansions of Helmholtz-like kernels with complex wavenumbers of the form k = (α + iβ)ϑ, with α = 0,±1 and β > 0, which, the paucity of available studies notwithstanding, arise for a wealth of different physical problems. It is suggested that a simple point-wise error indicator can provide an a-priori indication on the number N of terms to be employed in the Gegenbauer addition formula in order to achieve a prescribed accuracy when integrating single layer potentials over surfaces. For β ≥ 1 it is observed that the… More >

J. Tausch¹, J. Xiao²

CMES-Computer Modeling in Engineering & Sciences, Vol.58, No.3, pp. 221-246, 2010, DOI:10.3970/cmes.2010.058.221

Abstract A fast method for the computation of layer potentials that arise in acoustic scattering is introduced. The principal idea is to split the singular kernel into a smooth and a local part. The potential due to the smooth part is discretized by a Nyström method and is evaluated efficiently using a sequence of FFTs. The potential due to the local part is approximated by a truncated series in the mollification parameter. The smooth approximation of the kernel is obtained by multiplication of its Fourier transform with a filter. We will show that for a rational filter the smooth part and… More >

A. Takei¹, S. Yoshimura¹, H. Kanayama²

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.1, pp. 63-82, 2009, DOI:10.3970/cmes.2009.040.063

Abstract This paper describes a large-scale finite element analysis (FEA) for a high-frequency electromagnetic field of Maxwell equations including the displacement current. A stationary Helmholtz equation for the high-frequency electromagnetic field analysis is solved by considering an electric field and an electric scalar potential as unknown functions. To speed up the analysis, the hierarchical domain decomposition method (HDDM) is employed as a parallel solver. In this study, the Parent-Only type (Parallel processor mode: P-mode) of the HDDM is employed. In the P-mode, Parent processors perform the entire FEA. In this mode, all CPUs can be used without idling in an environment… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.2, pp. 179-198, 2008, DOI:10.3970/cmes.2008.033.179

Abstract Dirichlet boundary value problem of quasilinear elliptic equation is numerically solved by using a new concept of fictitious time integration method (FTIM). We introduce a fictitious time coordinate t by transforming the dependent variable u(x,y) into a new one by (1+t)u(x,y) =: v(x,y,t), such that the original equation is naturally and mathematically equivalently written as a quasilinear parabolic equation, including a viscous damping coefficient to enhance stability in the numerical integration of spatially semi-discretized equation as an ordinary differential equations set on grid points. Six examples of Laplace, Poisson, reaction diffusion, Helmholtz, the minimal surface, as well as the explosion… More >

T.Z. Desta¹, G. De Bruyne¹, J.-M. Aerts¹, M. Baelmans², D. Berckmans¹

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.2, pp. 61-70, 2008, DOI:10.3970/cmes.2008.031.061

Abstract This paper demonstrates the use of the concept of the local mean age of air (LMAA) to quantify ventilation effectiveness under bicycle rider's safety helmets. The specific objective is to study the effect of helmet openings on the resulting ventilation effectiveness. To quantify ventilation effectiveness using the concept of LMAA, dynamic tracer gas data are necessary. The data were generated using a Computational Fluid Dynamics (CFD) model. Two bicycle helmet designs were used and compared with respect to ventilation performance. The result showed that the helmet with more openings had better performance especially at the back of the head. The… More >

Chia-Cheng Tsai¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 151-162, 2008, DOI:10.3970/cmes.2008.027.151

Abstract In this paper we develop analytical particular solutions for the polyharmonic and the products of Helmholtz-type partial differential operators with Chebyshev polynomials at right-hand side. Our solutions can be written explicitly in terms of either monomial or Chebyshev bases. By using these formulas, we can obtain the approximate particular solution when the right-hand side has been represented by a truncated series of Chebyshev polynomials. These formulas are further implemented to solve inhomogeneous partial differential equations (PDEs) in which the homogeneous solutions are complementarily solved by the method of fundamental solutions (MFS). Numerical experiments, which include eighth order PDEs and three-dimensional… More >

H.B. Chen¹, D.J. Fu¹, P.Q. Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 85-98, 2007, DOI:10.3970/cmes.2007.020.085

Abstract Researches today show that, both approximation and dispersion errors are encountered by classical Galerkin FEM solutions for Helmholtz equation governing the harmonic wave propagation, which leads to numerical inaccuracies especially for high wave number cases. In this paper, Local Boundary Integral Equation Method (LBIEM) is firstly implemented to solve the boundary value problem of Helmholtz equation. Then the regularized LBIE is proposed to overcome the singularities of the boundary integrals in the LBIEM. Owing to the advantages of the Moving Least Square Approximation (MLSA), the frequency-dependent basis functions modified by the harmonic wave propagation solutions are easily adopted instead of… More >

Susom Dutta¹, A. Ramach,ra Murthy², Dookie Kim³, Pijush Samui⁴

CMC-Computers, Materials & Continua, Vol.53, No.2, pp. 157-174, 2017, DOI:10.3970/cmc.2017.053.167

Abstract In the present scenario, computational modeling has gained much importance for the prediction of the properties of concrete. This paper depicts that how computational intelligence can be applied for the prediction of compressive strength of Self Compacting Concrete (SCC). Three models, namely, Extreme Learning Machine (ELM), Adaptive Neuro Fuzzy Inference System (ANFIS) and Multi Adaptive Regression Spline (MARS) have been employed in the present study for the prediction of compressive strength of self compacting concrete. The contents of cement (c), sand (s), coarse aggregate (a), fly ash (f), water/powder (w/p) ratio and superplasticizer (sp) dosage have been taken as inputs… More >