On the Use of Sparsity in the Solution of Finite Element Systems of Equations By

Cover 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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