Theory and applications of the Analytic Element Method

Strack, Otto D. L.

doi:10.1029/2002rg000111

Cited by 88 publications

(89 citation statements)

References 40 publications

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“…Tais condições de contorno não são satisfeitas de forma exata, mas de forma tão precisa quanto possível para um dado número de graus de liberdade e natureza dos elementos. O escoamento irrotacional em aqüíferos de uma só camada dispõe de uma formulação bastante amadurecida no AEM e a precisão dos resultados depende somente do desempenho das máquinas utilizadas [14]. Passamos a discutir de maneira breve, modelos de elementos analíticos para aqüíferos de uma só camada [15,5].…”

Section: Formulação Do Métodounclassified

Acoplamento de Expressão Unidimensional de Recarga a Modelos de Elementos Analíticos

Batista¹,

Wendland²,

Schulz³

2005

TEMA - Tendências Em Matemática Aplicada E Computacional

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Resumo. Este trabalho diz respeitoà aplicação do Método de Elementos Analíticos, desenvolvido originariamente para domínios infinitos, a um problema de escoamento subterrâneo caracterizado em domínio semi-infinito. A aplicação de Elementos Analíticos a esses domínios exige a utilização de métodos auxiliares (por exemplo o método de imagens) que, em contra partida, eliminam a necessidade da utilização de elementos convencionais para a representação de efeitos regionais (por exemplo a recarga direta do aqüífero) dando assim lugarà utilização de expressões unidimensionais. A modelagem de problemas em meios porosos com essa técnica reproduz com precisão o campo de escoamento em regiões semi-infinitas.

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Section: Formulação Do Métodounclassified

Acoplamento de Expressão Unidimensional de Recarga a Modelos de Elementos Analíticos

Batista¹,

Wendland²,

Schulz³

2005

TEMA - Tendências Em Matemática Aplicada E Computacional

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“…The AEM has also been applied to boundary-value problems with geometries of circular arcs (Strack 1989), hyperbolic arcs (Strack 2003), Bezier curves (Le Grand 1999) and B-splines (Le Grand 2003.…”

Section: Introductionmentioning

confidence: 99%

“…Recent advances in the Analytic Element Method (AEM) have produced formulations using analytic, closed-form integration techniques for Cauchy integrals of higher order strength (large M ) along straight lines (Janković & Barnes 1999;Strack 2003;Steward et al 2005). The AEM has also been applied to boundary-value problems with geometries of circular arcs (Strack 1989), hyperbolic arcs (Strack 2003), Bezier curves (Le Grand 1999) and B-splines (Le Grand 2003.…”

Section: Introductionmentioning

confidence: 99%

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Analytic formulation of Cauchy integrals for boundaries with curvilinear geometry

et al. 2007

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A general framework for analytic evaluation of singular integral equations with a Cauchy kernel is developed for higher order line elements of curvilinear geometry. This extends existing theory which relies on numerical integration of Cauchy integrals since analytic evaluation is currently published only for straight lines, and circular and hyperbolic arcs. Analytic evaluation of Cauchy integrals along straight elements is presented to establish a context coalescing new developments within the existing body of knowledge. Curvilinear boundaries are partitioned into sectionally holomorphic elements that are conformally mapped from a local curvilinear Z-plane to a straight line in the Z-plane. Cauchy integrals are evaluated in these planes to achieve a simple representation of the complex potential using Chebyshev polynomials and a Taylor series expansion of the conformal mapping. Bell polynomials and the Faà di Bruno formula provide this Taylor series for mappings expressed as inverse mappings and/or compositions. Examples illustrate application of the general framework to boundary-value problems with boundaries of natural coordinates, Bezier curves and B-splines. Strings formed by the union of adjacent curvilinear elements form a large class of geometries along which Dirichlet and/or Neumann conditions may be applied. This provides a framework applicable to a wide range of fields of study including groundwater flow, electricity and magnetism, acoustic radiation, elasticity, fluid flow, air flow and heat flow.

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“…Of particular importance for transport modeling, the mass balance on water is exact everywhere and the method does not require the use of a computational grid or mesh. Extended discussions of the mathematical principles behind the analytic element method may be found elsewhere [Strack, 1989;Haitjema, 1995;Janković, 1997;Strack, 2003].…”

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confidence: 99%

Finite element transport modeling using analytic element flow solutions

Craig

Rabideau

2006

Water Resources Research

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[1] Finite element methods for solute transport simulation typically use a discrete representation of the flow domain obtained from a finite element solution of the associated groundwater flow problem. Velocity, saturated thickness, and components of the dispersion coefficient tensor are represented as a set of nodal and/or element-averaged values. In contrast, the analytic element method (AEM) provides continuous mesh-independent solutions for these variables. In this paper, a set of techniques for using two-dimensional AEM flow solutions as the basis of finite element solute transport models is introduced. First, a general AEM-based discretization approach is presented that addresses the existence of curved boundaries, singularities, and discontinuities in vertically averaged concentration. Second, residual integration methods that handle continuous parameters with internal and boundary singularities are developed and evaluated. Third, an approach is introduced for handling internal discontinuities in concentration across certain analytic elements. This new approach uses a nonstandard mesh topology and a new formulation for internal coupled boundary conditions. The AEM-based transport simulation methods introduced in this paper are demonstrated to be robust and accurate for a variety of test problems.

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Theory and applications of the Analytic Element Method

Cited by 88 publications

References 40 publications

Acoplamento de Expressão Unidimensional de Recarga a Modelos de Elementos Analíticos

Acoplamento de Expressão Unidimensional de Recarga a Modelos de Elementos Analíticos

Analytic formulation of Cauchy integrals for boundaries with curvilinear geometry

Finite element transport modeling using analytic element flow solutions

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