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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 25 May 2020 00:30:58 GMT2020-05-25T00:30:58ZOn the physical interpretation of fractional diffusion
http://hdl.handle.net/10985/13278
On the physical interpretation of fractional diffusion
NADAL, Enrique; ABISSET-CHAVANNE, Emmanuelle; CUETO, Elias; CHINESTA, Francisco
Even if the diffusion equation has been widely used in physics and engineering, and its physical content is well understood, some variants of it escape fully physical understanding. In particular, anormal diffusion appears in the so-called fractional diffusion equation, whose main particularity is its non-local behavior, whose physical interpretation represents the main part of the present work.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/132782018-01-01T00:00:00ZNADAL, EnriqueABISSET-CHAVANNE, EmmanuelleCUETO, EliasCHINESTA, FranciscoEven if the diffusion equation has been widely used in physics and engineering, and its physical content is well understood, some variants of it escape fully physical understanding. In particular, anormal diffusion appears in the so-called fractional diffusion equation, whose main particularity is its non-local behavior, whose physical interpretation represents the main part of the present work.Proper generalized decomposition solutions within a domain decomposition strategy
http://hdl.handle.net/10985/13823
Proper generalized decomposition solutions within a domain decomposition strategy
HUERTA, Antonio; NADAL, Enrique; CHINESTA, Francisco
Domain decomposition strategies and proper generalized decomposition are efficiently combined to obtain a fast evaluation of the solution approximation in parameterized elliptic problems with complex geometries. The classical difficulties associated to the combination of layered domains with arbitrarily oriented midsurfaces, which may require in-plane–out-of-plane techniques, are now dismissed. More generally, solutions on large domains can now be confronted within a domain decomposition approach. This is done with a reduced cost in the offline phase because the proper generalized decomposition gives an explicit description of the solution in each subdomain in terms of the solution at the interface. Thus, the evaluation of the approximation in each subdomain is a simple function evaluation given the interface values (and the other problem parameters). The interface solution can be characterized by any a priori user-defined approximation. Here, for illustration purposes, hierarchical polynomials are used. The repetitiveness of the subdomains is exploited to reduce drastically the offline computational effort. The online phase requires solving a nonlinear problem to determine all the interface solutions. However, this problem only has degrees of freedom on the interfaces and the Jacobian matrix is explicitly determined. Obviously, other parameters characterizing the solution (material constants, external loads, and geometry) can also be incorporated in the explicit description of the solution.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/138232018-01-01T00:00:00ZHUERTA, AntonioNADAL, EnriqueCHINESTA, FranciscoDomain decomposition strategies and proper generalized decomposition are efficiently combined to obtain a fast evaluation of the solution approximation in parameterized elliptic problems with complex geometries. The classical difficulties associated to the combination of layered domains with arbitrarily oriented midsurfaces, which may require in-plane–out-of-plane techniques, are now dismissed. More generally, solutions on large domains can now be confronted within a domain decomposition approach. This is done with a reduced cost in the offline phase because the proper generalized decomposition gives an explicit description of the solution in each subdomain in terms of the solution at the interface. Thus, the evaluation of the approximation in each subdomain is a simple function evaluation given the interface values (and the other problem parameters). The interface solution can be characterized by any a priori user-defined approximation. Here, for illustration purposes, hierarchical polynomials are used. The repetitiveness of the subdomains is exploited to reduce drastically the offline computational effort. The online phase requires solving a nonlinear problem to determine all the interface solutions. However, this problem only has degrees of freedom on the interfaces and the Jacobian matrix is explicitly determined. Obviously, other parameters characterizing the solution (material constants, external loads, and geometry) can also be incorporated in the explicit description of the solution.