Guaranteed lower eigenvalue bounds for the Euler-Bernoulli beam are obtained from interpolation error estimates with known constants, yielding two-sided bounds that converge for both linear and nonlinear Gao beam models.
The- ory, Approximation, and Computation
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Shape optimization of Maxwell eigenvalues via adjoint sensitivities on a reference domain, solved with a damped inverse BFGS method and mixed finite elements.
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Two-sided eigenvalue bounds for the Euler-Bernoulli beam
Guaranteed lower eigenvalue bounds for the Euler-Bernoulli beam are obtained from interpolation error estimates with known constants, yielding two-sided bounds that converge for both linear and nonlinear Gao beam models.
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Numerical Eigenvalue Optimization by Shape-Variations for Maxwell's Eigenvalue Problem
Shape optimization of Maxwell eigenvalues via adjoint sensitivities on a reference domain, solved with a damped inverse BFGS method and mixed finite elements.