Monday, February 1, 1999, 4:00pm, 120 Physics

Yalchin Efendiev (Cal Tech)

- The multiscale finite element method has been developed to capture the large scale solutions of elliptic equations with highly oscillatory coefficients. This is accomplished by constructing the multiscale base functions from the local solutions of elliptic operator. The construction of the base functions is decoupled from element to element; thus the method is well adapted to massively parallel computers. The study of MsFEM reveals that the leading error is caused by the "resonant sampling", which leads to large error when the mesh size is close to the small scale of the continuous problem. Similar difficulties also arise in numerical upscaling methods. An oversampling technique has been developed to alleviate this difficulty. A consequence of the over-sampling is that the method is no longer conforming. The applications of MsFEM to upscaling of reservoir properties will be discussed. Hosts: John Trangenstein and Bill Allard

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