J. Trevelyan¹and G. Coates¹

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 147-170, 2010, DOI:10.3970/cmes.2010.055.147

Abstract The terminology "wave boundary elements" relates to boundary elements enriched in the Partition of Unity sense by a multiple plane wave basis for the analysis of the propagation of short wavelength waves. This paper presents a variant of this approach in which the plane wave basis is selected adaptively according to an error indicator. The error indicator is residual based, and exhibits useful local and global properties. Model improvement in each adaptive iteration is carried out by the addition of new plane waves with no h-refinement. The convergence properties of the scheme are demonstrated. More >

Chein-Shan Liu¹

CMC-Computers, Materials & Continua, Vol.18, No.1, pp. 1-20, 2010, DOI:10.3970/cmc.2010.018.001

Abstract We are concerned with the reconstruction of an unknown space-dependent rigidity coefficient in a wave equation. This problem is known as one of the inverse scattering problems. Based on a two-point Lie-group equation we develop a Lie-group adaptive method (LGAM) to solve this inverse scattering problem through iterations, which possesses a special character that by using onlytwo boundary conditions and two initial conditions, as those used in the direct problem, we can effectively reconstruct the unknown rigidity function by aself-adaption between the local in time differential governing equation and the global in time algebraic Lie-group More >

Hrvoje Gotovac¹, Vedrana Kozulić², Blaž Gotovac¹

CMC-Computers, Materials & Continua, Vol.15, No.3, pp. 173-198, 2010, DOI:10.3970/cmc.2010.015.173

Abstract The space-time Adaptive Fup Collocation Method (AFCM) for solving boundary-initial value problems is presented. To solve the one-dimensional initial boundary value problem, we convert the problem into a two-dimensional boundary value problem. This quasi-boundary value problem is then solved simultaneously in the space-time domain with a collocation technique and by using atomic Fup basis functions. The proposed method is a generally meshless methodology because it requires only the addition of collocation points and basis functions over the domain, instead of the classical domain discretization and numerical integration. The grid is adapted progressively by setting the More >

Z. Bittnar¹, B. Patzák¹, D. Rypl¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.13, No.3, pp. 55-56, 2009, DOI:10.3970/icces.2009.013.055

Abstract This paper deals with the design of framework for adaptive FEM analysis with dynamic load balancing in nondedicated parallel cluster computing environments. It describes in detail the structure and design of individual components of the framework.
The application of adaptivity paradigm to engineering problems results in computationally very demanding analysis in terms of both computational time and computer resources (memory, disk space, etc.). These demands can be alleviated by performing the analysis in a parallel computing environment. Typical parallel application decreases the demands on memory and other resources by spreading the task over several mutually… More >

Nicolas Ali Libre^1,2, Arezoo Emdadi², Edward J. Kansa^3,4, Mohammad Shekarchi², Mohammad Rahimian²

CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.2, pp. 161-190, 2009, DOI:10.3970/cmes.2009.050.161

Abstract We present a wavelet based adaptive scheme and investigate the efficiency of this scheme for solving nearly singular potential PDEs over irregularly shaped domains. For a problem defined over Ω∈ℜ^d, the boundary of an irregularly shaped domain, Γ, is defined as a boundary curve that is a product of a Heaviside function along the normal direction and a piecewise continuous tangential curve. The link between the original wavelet based adaptive method presented in Libre, Emdadi, Kansa, Shekarchi, and Rahimian (2008, 2009) or LEKSR method and the generalized one is given through the use of simple Heaviside More >

Alexandre de Castro^1,2, Carlos Frederico Fronza², Domingos Alves^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.45, No.1, pp. 83-96, 2009, DOI:10.3970/cmes.2009.045.083

Abstract Immunological systems have been an abundant inspiration to contemporary computer scientists. Problem solving strategies, stemming from known immune system phenomena, have been successfully applied to chall enging problems of modern computing. Simulation systems and mathematical modeling are also beginning use to answer more complex immunological questions as immune memory process and duration of vaccines, where the regulation mechanisms are not still known sufficiently (Lundegaard, Lund, Kesmir, Brunak, Nielsen, 2007). In this article we studiedin machinaa approach to simulate the process of antigenic mutation and its implications for the process of memory. Our results have suggested More >

A. Brancati¹, M. H. Aliabadi¹, I. Benedetti^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.2, pp. 149-172, 2009, DOI:10.3970/cmes.2009.043.149

Abstract In this paper a new Rapid Acoustic Boundary Element Method (RABEM) is presented using a Hierarchical GMRES solver for 3D acoustic problems. The Adaptive Cross Approximation is used to generate both the system matrix and the right hand side vector. The ACA is also used to evaluate the potential and the particle velocity values at selected internal points. Two different GMRES solution strategies (without preconditioner and with a block diagonal preconditioner) are developed and tested for low and high frequency problems. Implementation of different boundary conditions (i.e. Dirichlet, Neumann and mixed Robin) is also described. More >

G. C. Bourantas¹, E. D. Skouras^2,3,4, G. C. Nikiforidis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.1, pp. 1-26, 2009, DOI:10.3970/cmes.2009.043.001

Abstract The extent of application of meshfree methods based on point collocation (PC) techniques with adaptive support domain for strong form Partial Differential Equations (PDE) is investigated. The basis functions are constructed using the Moving Least Square (MLS) approximation. The weak-form description of PDEs is used in most MLS methods to circumvent problems related to the increased level of resolution necessary near natural (Neumann) boundary conditions (BCs), dislocations, or regions of steep gradients. Alternatively, one can adopt Radial Basis Function (RBF) approximation on the strong-form of PDEs using meshless PC methods, due to the delta function… More >

Shang Ma¹, Xiong Zhang^1,2, Yanping Lian¹, Xu Zhou³

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.2, pp. 101-124, 2009, DOI:10.3970/cmes.2009.039.101

Abstract Numerical simulation of high explosive explosion problems is a big challenge to traditional numerical methods because explosion usually involves extremely large deformation and multi-material interaction of different phases. Recently developed meshfree methods show much advantages over mesh-based method for problems associated with very large deformation. Some of them have been successfully applied to impact and explosion problems, such as smoothed particle hydrodynamics (SPH). Similar to SPH, material point method (MPM) is an efficient meshfree particle method solving continuum problems. With combination of the advantages of Eulerian and Lagrangian methods, MPM is a promising numerical tool… More >

Leevan Ling¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.8, No.4, pp. 133-138, 2008, DOI:10.3970/icces.2008.008.133

Abstract The history of meshless collocation methods featured plenty of nicely calculated practical solutions, but a solid mathematical basis was long missing for the most popular asymmetric technique introduced by E. Kansa. Thus the impact of this work will be to supply a lasting mathematical foundation which will also improve our general understanding of such technique. Our previous research gave a convergent algorithm. More >