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- Analytic_element_method abstract "The analytic element method (AEM) is a numerical method used for the solution of partial differential equations. It was initially developed by O.D.L. Strack at the University of Minnesota. It is similar in nature to the boundary element method (BEM), as it does not rely upon discretization of volumes or areas in the modeled system; only internal and external boundaries are discretized. One of the primary distinctions between AEM and BEMs is that the boundary integrals are calculated analytically. The analytic element method has been applied to problems of groundwater flow governed by a variety of linear partial differential equations including the Laplace, the Poisson equation, the modified Helmholtz equation, the heat equation, and the biharmonic equations. The basic premise of the analytic element method is that, for linear differential equations, elementary solutions may be superimposed to obtain more complex solutions. A suite of 2D and 3D analytic solutions (\"elements\") are available for different governing equations. These elements typically correspond to a discontinuity in the dependent variable or its gradient along a geometric boundary (e.g., point, line, ellipse, circle, sphere, etc.). This discontinuity has a specific functional form (usually a polynomial in 2D) and may be manipulated to satisfy Dirichlet, Neumann, or Robin (mixed) boundary conditions. Each analytic solution is infinite in space and/or time. In addition, each analytic solution contains degrees of freedom (coefficients) that may be calculated to meet prescribed boundary conditions along the element's border. To obtain a global solution (i.e., the correct element coefficients), a system of equations is solved such that the boundary conditions are satisfied along all of the elements (using collocation, least-squares minimization, or a similar approach). Notably, the global solution provides a spatially continuous description of the dependent variable everywhere in the infinite domain, and the governing equation is satisfied everywhere exactly except along the border of the element, where the governing equation is not strictly applicable due to the discontinuity.The ability to superpose numerous elements in a single solution means that analytical solutions can be realized for arbitrarily complex boundary conditions. That is, models that have complex geometries, straight or curved boundaries, multiple boundaries, transient boundary conditions, multiple aquifer layers, piecewise varying properties and continuously varying properties can be solved. Elements can be implemented using far-field expansions such that model containing many thousands of elements can be solved efficiently to high precision.".
- Analytic_element_method wikiPageExternalLink 9780123847058.
- Analytic_element_method wikiPageExternalLink Main_Page.
- Analytic_element_method wikiPageExternalLink www.fittsgeosolutions.com.
- Analytic_element_method wikiPageExternalLink howtoorder.html.
- Analytic_element_method wikiPageID "2289219".
- Analytic_element_method wikiPageLength "3959".
- Analytic_element_method wikiPageOutDegree "15".
- Analytic_element_method wikiPageRevisionID "678582150".
- Analytic_element_method wikiPageWikiLink Biharmonic_equation.
- Analytic_element_method wikiPageWikiLink Boundary_element_method.
- Analytic_element_method wikiPageWikiLink Category:Hydrology_models.
- Analytic_element_method wikiPageWikiLink Category:Numerical_differential_equations.
- Analytic_element_method wikiPageWikiLink Collocation_method.
- Analytic_element_method wikiPageWikiLink Groundwater_flow_equation.
- Analytic_element_method wikiPageWikiLink Heat_equation.
- Analytic_element_method wikiPageWikiLink Laplaces_equation.
- Analytic_element_method wikiPageWikiLink Least_squares.
- Analytic_element_method wikiPageWikiLink Linear_differential_equation.
- Analytic_element_method wikiPageWikiLink Numerical_analysis.
- Analytic_element_method wikiPageWikiLink Partial_differential_equation.
- Analytic_element_method wikiPageWikiLink Poissons_equation.
- Analytic_element_method wikiPageWikiLink University_of_Minnesota.
- Analytic_element_method wikiPageWikiLinkText "Analytic Element Method".
- Analytic_element_method wikiPageWikiLinkText "Analytic element method".
- Analytic_element_method wikiPageWikiLinkText "analytic element method".
- Analytic_element_method wikiPageUsesTemplate Template:Analysis-stub.
- Analytic_element_method wikiPageUsesTemplate Template:Cite_book.
- Analytic_element_method wikiPageUsesTemplate Template:Comp-sci-stub.
- Analytic_element_method wikiPageUsesTemplate Template:Numerical_PDE.
- Analytic_element_method subject Category:Hydrology_models.
- Analytic_element_method subject Category:Numerical_differential_equations.
- Analytic_element_method hypernym Method.
- Analytic_element_method type Model.
- Analytic_element_method type Software.
- Analytic_element_method type Model.
- Analytic_element_method type Redirect.
- Analytic_element_method comment "The analytic element method (AEM) is a numerical method used for the solution of partial differential equations. It was initially developed by O.D.L. Strack at the University of Minnesota. It is similar in nature to the boundary element method (BEM), as it does not rely upon discretization of volumes or areas in the modeled system; only internal and external boundaries are discretized.".
- Analytic_element_method label "Analytic element method".
- Analytic_element_method sameAs Q4751128.
- Analytic_element_method sameAs m.0715c4.
- Analytic_element_method sameAs Q4751128.
- Analytic_element_method wasDerivedFrom Analytic_element_method?oldid=678582150.
- Analytic_element_method isPrimaryTopicOf Analytic_element_method.