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7 votes
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The nitty-gritty details of augmented Lagrangian methods

My favorite reference on this is Constrained Optimization and Lagrange Multiplier Methods by Bertsekas. It's a little old (1982) but I haven't seen any other reference that describes many of the ...
Daniel Shapero's user avatar
3 votes

inclined/general Dirichlet boundary conditions

Bill Greene presents the point of view of how things have been done traditionally. The "modern" way is to add "constraints" to your linear system which, in the current case, would ...
Wolfgang Bangerth's user avatar
3 votes
Accepted

inclined/general Dirichlet boundary conditions

The traditional way to handle this type of boundary condition is to create a transformed coordinate system at node 3 so that one of its axes is along the direction you want to constrain. You use the ...
Bill Greene's user avatar
  • 6,119
2 votes

Applying displacement control loading using lagrange multipliers in the material non-linear finite element method

The addition of the Lagrange multiplier term is an unnecessary complication in this case, so let's just consider the simpler root finding problem $$ F(u) = \frac12 u^TK(u)u - fu = 0. $$ Your ...
Wolfgang Bangerth's user avatar

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