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您的检索式：作者名="Michael Presho"
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| 1 | Generalized Multiscale Finite Element Methods.Nonlinear Elliptic Equations显示文摘In this paper we use the Generalized Multiscale Finite Element Method(GMsFEM)framework,introduced in[26],in order to solve nonlinear elliptic equations with high-contrast coefficients.The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation.With this convention,we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin(CG)or discontinuous Galerkin(DG)global formulations.Here,we use Symmetric Interior Penalty Discontinuous Galerkin approach.Both methods yield a predictable error decline that depends on the respective coarse space dimension,and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. | Yalchin Efendiev Juan Galvis Guanglian Li Michael Presho | 2014 | Communications in Computational Physics2014，15，3： | 0 |
| 2 | Multilevel Markov Chain Monte Carlo Method for High-Contrast Single-Phase Flow Problems显示文摘In this paper we propose a general framework for the uncertainty quantification of quantities of interest for high-contrast single-phase flow problems.It is based on the generalized multiscale finite element method(GMsFEM)and multilevel Monte Carlo(MLMC)methods.The former provides a hierarchy of approximations of different resolution,whereas the latter gives an efficient way to estimate quantities of interest using samples on different levels.The number of basis functions in the online GMsFEM stage can be varied to determine the solution resolution and the computational cost,and to efficiently generate samples at different levels.In particular,it is cheap to generate samples on coarse grids but with low resolution,and it is expensive to generate samples on fine grids with high accuracy.By suitably choosing the number of samples at different levels,one can leverage the expensive computation in larger fine-grid spaces toward smaller coarse-grid spaces,while retaining the accuracy of the final Monte Carlo estimate.Further,we describe a multilevel Markov chain Monte Carlo method,which sequentially screens the proposal with different levels of approximations and reduces the number of evaluations required on fine grids,while combining the samples at different levels to arrive at an accurate estimate.The framework seamlessly integrates the multiscale features of the GMsFEM with the multilevel feature of the MLMC methods following the work in[26],and our numerical experiments illustrate its efficiency and accuracy in comparison with standard Monte Carlo estimates. | Yalchin Efendiev Bangti Jin Michael Presho Xiaosi Tan | 2015 | Communications in Computational Physics2015，17，1： | 0 |
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