On the Use of Sparsity in the Solution of Finite Element Systems of Equations By
On the Use of Sparsity in the Solution of Finite Element Systems of Equations By
Olof B Widlund
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R"ther execution of the CholeBky factorisation and. Ewltchojs to a reliable pivoting stp&tegy. In using a well- wrltteri program of this kind tot- a jsatris oraered by one cf the dissection algox'ithras m^ f-ould be •col'iiUaent that pivoti -ig vrill be postponed till a sta^e when only a i-alatively small number of variables remain tc- be ellmlnateci. f J , ^. I. . _, . Nonlinear Frpbl^^ Ai'; Is weni-knowa. , tha solution oi" the linear syritsm of equations Ax -* h^ A positive definite ^ symmet...ric, can equali;/ • well be ch&rav-jtc-riKad as tke. Yector. X TAfhich . Minimizes (1/2} (x Ay - 2b x)- We villi no>: consider the jninisatlon of a nonquadratift function F(x) mider fche asaiimptions that the Hessian laatris GCx) >■'■■ f|~r-v^'^* ^s lirjiforaly positive deflxtit^e ex^a-c, • . . . . 3i-id haa the satna finite element spas»8ity strvictiire far all x. In particular i we will explore the use of certain v&riablej metric mathodr*. The ntandard variable metric methods, such ■.
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