hmwk_2_2010

hmwk_2_2010 - UNIVERSITY OF NOTRE DAME Department of Civil...

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UNIVERSITY OF NOTRE DAME Department of Civil Engineering and Geological Sciences CE 30125 September 9, 2007 J.J. Westerink Due: September 15, 2007 Homework Set #2 Backgound: Many computational codes solving problems in mechanics, optimization, and/or forecasting will result in very large systems of algebraic equations of the form that need to be solved. Direct methods are available that rely on systematically re-arranging the equations into much more convenient forms that allow for straight forward solutions. The cost of the solution is a vital factor, for example Gauss elimination it cost operations where N is the size of the fully populated matrix. The largest portion of the computa- tional cost lies in manipulating the matrix. However, for many cases of interest we must solve systems of the form where the matrix stays the same and many right hand side load vectors must be solved. In this case, a formal decomposition of the matrix into a product of lower and upper triangular matrices can be performed once without operating on the right hand side vector. This then allows for the forward and backward solution sweeps to be applied to many right hand sides at a cost of . This dramatically reduces the cost of
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This note was uploaded on 03/02/2012 for the course CE 30125 taught by Professor Westerink,j during the Fall '08 term at Notre Dame.

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hmwk_2_2010 - UNIVERSITY OF NOTRE DAME Department of Civil...

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