Fast r-adaptivity for multiple queries of heterogeneous stochastic materialfields
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Estadístiques de LA Referencia / Recolecta
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/333995
Tipus de documentText en actes de congrés
Data publicació2015
EditorCIMNE
Condicions d'accésAccés obert
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Abstract
The Monte Carlo approach in stochastic modeling requires multiple queries to numerical (typicallyfinite element) solutions of similar problems. In the case of random material fields, only the materialproperties vary between different realizations, often representing perturbations of a simple materialdescription around a reference configuration (typically a uniform material field). The differentinstances of the Monte Carlo sampling are usually computed with the same finite element mesh,which is designed to provide a reasonable accuracy in the case of the average material field.However, this mesh is not accounting for the actual realization of the stochastic material field andtherefore it does not obtain the maximum accuracy that could be achieved with the computationalresources employed. The possibility of designing a new mesh from scratch for each Monte Carlorealization is not realistic: the computational cost of redesigning the mesh based on the fluctuatingmaterial field is unaffordable when the number of Monte Carlo samples increases. Moreover, theperturbations in the material field are not expected to require a drastically different mesh. Note forinstance, that the local mesh refinement resolving the patterns in the solution associated with thegeometrical features of the domain are kept constant all along the Monte Carlo process. The strategyproposed in this paper consists in modifying for each realization a mesh designed to be efficient inthe reference (unperturbed) case. The mesh is then modified following an r-adaptive scheme at eachMonte Carlo realization. The mesh adaption is performed on the basis of simple criteria accountingfor the actual (perturbed) material field. Note that the r-adaptive approach suits the needs of thecurrent scope (optimal distribution of the computational resources, having set a priori the number ofdegrees-of-freedom) but does not allow guaranteeing the final accuracy of the results obtained.
CitacióCottereau, R.; Díez, P. Fast r-adaptivity for multiple queries of heterogeneous stochastic materialfields. A: ADMOS 2015. CIMNE, 2015, p. 76.
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