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[wip] Finite element integration refactor #141

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@dbeurle dbeurle commented Jan 6, 2019

This PR adds several key features in order to move away from 'full' and 'reduced' element integration schemes as this is not flexible enough to integrate different bilinear forms, resulting in rank deficient mass like matrices that arise in dynamic analysis and in reaction-diffusion type problems.

  • Uncouple shape functions and quadrature schemes
  • Add several new quadrature schemes
  • Split quadrature into their own namespaces
  • Add fem::integral that composes interpolation and numerical_quadrature types
  • Check minimum degree of quadrature based on shape function and (bi)linear form

Some fallout from this refactor is that the patch recovery logic is not split into it's own class that should be responsible for performing the integration point to nodal point extrapolation using the shape function (or similar).

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