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In this procedure, the unknown macroscopic constitutive relationship is searched by solving a local finite element problem at the microscale.
In the present approach, the unknown constitutive relationship at the macroscale is obtained by solving a local finite element problem at the microscale.
The weights in the linear combination are derived through the linearity preserving approach and can be obtained by solving a local linear system whose solvability is rigorously discussed.
Our algorithm acts variationally on tensor products and updates the tensors one after another by solving a local nonlinear optimization problem.
Moreover, through an appropriate choice of the weighting function, the closure terms can be obtained by solving a local closure problem on a unit cell of the periodic structures.
The parabolic reconstruction of the interface in a given computational cell is obtained by solving a local non-linear minimisation problem, and only requires additional information from two neighbouring cells.
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The basic idea is to rescale space and time so that the front becomes a sharp interface whose location can be determined by solving a corresponding local Hamilton-Jacobi equation.
For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over dual-grid cells.
The analytical solutions of the local problems are obtained by solving a system of partial differential equations.
The local impulse gain matrices can be designed by solving a set of LMIs.
The alliance with McDonnell Douglas thus solved a local business problem.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com