Can I read The Construction of the Coarse de Rham Complexes with Improved Approximation Properties on EtoBox?

The Construction of the Coarse de Rham Complexes with Improved Approximation Properties by Ilya V. Lashuk; Panayot S. Vassilevski is a Engineering article available to read on EtoBox.

What is The Construction of the Coarse de Rham Complexes with Improved Approximation Properties about?

## Abstract. We present two novel coarse spaces (__H^1^__- and H ( curl ) $H(\operatorname{curl})$ -conforming) based on element agglomeration on unstructured tetrahedral meshes. Each __H^1^__-conforming coarse basis function is continuous and piecewise-linear with respect to an original tetrahedral mesh. The H ( curl ) $H(\operatorname{curl})$ -conforming coarse space is a subspace of the lowest order Nédélec space of the first type. The __H^1^__-conforming coarse space exactly interpolates affine functions on each agglomerate. The H ( curl ) $H(\operatorname{curl})$ -conforming coarse space exactly interpolates vector constants on each agglomerate. Combined with the H ( div ) $H(\operatorname{div})$ - and __L~2~__-conforming spaces developed previously in [Numer. Linear Algebra Appl. 19 (2012), 414–426], the newly constructed coarse spaces form a sequence (with respect to exterior derivatives) which is exact as long as the underlying sequence of fine-grid spaces is exact. The constructed coarse spaces inherit the approximation and stability properties of the underlying fine-grid spaces supported by our numerical experiments. The new coarse spaces, in addition to multigrid, can be

Who reads The Construction of the Coarse de Rham Complexes with Improved Approximation Properties?

Author

Ilya V. Lashuk; Panayot S. Vassilevski

Publisher

Walter de Gruyter GmbH

Published

2014

Language

EN

Field

Engineering (Physical Sciences)