What question did this study set out to answer?

The aim is to establish realistic upper and lower bounds on the eigenvalues of the fully consistent mass matrix using unassembled finite-element equations.

October 1, 1987IMA Journal of Numerical Analysis

Realistic Eigenvalue Bounds for the Galerkin Mass Matrix

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Authors

AWAndy WathenRutherford Appleton Laboratory

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Implication

Randomized trial establishes realistic bounds on eigenvalues in finite-element methods, suggesting effective preconditioning techniques.

Key Points

The aim is to establish realistic upper and lower bounds on the eigenvalues of the fully consistent mass matrix using unassembled finite-element equations.
Utilized element-by-element analysis to derive eigenvalue bounds for the mass matrix in various finite elements.
Conducted independent calculations on different types of finite elements across one, two, and three dimensions.
Demonstrated independence of certain bounds from mesh irregularity.
Identified realistic upper and lower bounds for eigenvalues of the mass matrix of various finite-element types.
Showed that the preconditioned conjugate-gradient method is effective and rapid for solving Galerkin mass-matrix equations.
Provided examples where specific bounds are attained.

Cite This Study

Andy Wathen (1987) studied this question.

synapsesocial.com/papers/6a109a11d478ddac0ffd4133 https://doi.org/10.1093/imanum/7.4.449

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Realistic Eigenvalue Bounds for the Galerkin Mass Matrix

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Implication

Key Points

Cite This Study

Realistic Eigenvalue Bounds for the Galerkin Mass Matrix

Discussion

Member takes

Implication

Key Points

Cite This Study

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