TITLE:

HIGH ORDER DIFFERENTIAL OPERATORS AND THE SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS

DATE:

Friday, April 17th, 2009

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Jose Castillo, Director / Professor, Computational Science Research Center, San Diego State University

ABSTRACT:

Mimetic Operators satisfy a discrete analog of the divergence theorem and  they are used to create/design conservative/reliable numerical representations to continuous models. We will present a methodology to construct mimetic versions of the divergence and gradient operators which exhibit high order of accuracy at the grid interior as well as at the boundaries. As a case of study, we will show the construction of fourth order operators in a one-dimensional staggered grid. Mimetic conditions on discrete operators are stated using matrix analysis and the overall high order of accuracy determines the bandwidth parameter. This contributes to a marked clarity with respect to earlier approaches of construction. As test cases, we will solve 2-D elliptic equations with full tensor coefficients arising from oil reservoir models. Additionally, applications to elastic wave propagation under free surface and shear rupture boundary conditions will be given.

HOST:

Ricardo Carretero

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