Higher Order Multiscale Finite Element Method for Heat Transfer Modeling

. 2021 Jul 8;14(14):3827. doi: 10.3390/ma14143827

Algorithm 1 Solve a heat transfer problem within a heterogeneous domain.

Require: define the problem (heterogeneous domain and boundary conditions)
Ensure: a coarse mesh and an appropriate refinement of each coarse element
for n=1 to

N e l

do {loop over coarse mesh elements}
for m=1 to M do {loop over n-th element shape functions}
solve local problem (5) in the n-th element for the m-th shape function
end for
compute

K_{H}

and

f_{H}

for the n-th element
end for
solve the coarse mesh problem using the effective matrices

K_{H}

and vectors

f_{H}