Hi Martin,
unless you want to use a direct or parallel solver or have direct access
to the entries of the modified matrix you should be able to use the
FilteredMatrix class which is "a wrapper for linear systems of equations
with simple equality constraints fixing individual degrees of freedom to
a certain value such as when using Dirichlet boundary values." It was
implemented for cases when "one would like to have the ability to solve
multiply with the same matrix in ... or time dependent problems, without
having to re-assemble the matrix or copy it to temporary matrices with
which one then can work."
Best, Johannes
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