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MIT2_092F09_lec13 - 2.092/2.093 Finite Element Analysis of...

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2.092/2.093 Finite Element Analysis of Solids & Fluids I Fall ‘09 Lecture 13 - Physical Explanation of Gauss Elimination Prof. K. J. Bathe MIT OpenCourseWare Reading assignment: Sections 8.1, 8.2 Gauss elimination is the direct method of solution, which includes: LDL T factorization; sparse techniques Wavefront method Substructuring, super-element techniques, etc. Static condensation Example Reading assignment: Section 8.2.1 5 4 1 0 u 1 0 u 2 u 3 = 4 6 4 4 1 1 0 1 0 6 4 4 1 5 Let’s perform Gauss elimination on this system. Step 1: Add/subtract multiples of row 1 to the other rows to obtain: u 4 0 5 4 1 0 0 u 1 = 0 14 16 1 1 0 u 2 u 3 5 5 16 29 0 5 5 4 0 1 4 5 u 4 0 We used 5 u 1 4 u 2 + u 3 = 0 to eliminate u 1 from the second
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