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Point Collocation and Further Simplifications
1990The present chapter is devoted to simplifications of the Galerkin method. With little effort the complexity can be reduced one order of magnitude by introducing “engineering” approximations. It turns out that with well chosen stratagems the accuracy remains essentially equal to what can be obtained with the Galerkin method.
Patrick Dewilde, Zhen-Qui Ning
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Collocation at Gauss Points as a Discretization in Optimal Control
SIAM Journal on Control and Optimization, 1979Collocation at Gauss points is shown to be a high order accurate discretization of certain unconstrained optimal control problems. Best possible convergence rates are established along with superconvergence results.
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A meshless point collocation treatment of transient bioheat problems
International Journal for Numerical Methods in Biomedical Engineering, 2014SUMMARYA meshless numerical method is proposed for the solution of the transient bioheat equation in two and three dimensions. The Pennes bioheat equation is extended in order to incorporate water evaporation, tissue damage, and temperature‐dependent tissue properties during tumor ablation.
G C, Bourantas +3 more
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The Richardson Extrapolation Process with a Harmonic Sequence of Collocation Points
SIAM Journal on Numerical Analysis, 2000The author studies the problem: Let a function \(A(y)\) be known and hence computable for \(00\), the variable \(y\) being continuous or discrete. The author assumes that \(A(y)\) has an asymptotic expansion of the form \[ A(y)\sim A+ \sum_{k=1}^\infty \alpha_k y^{\sigma_k} \quad\text{as}\quad y\to 0+, \] where \(\sigma_k\) are known scalars satisfying
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On a misconception involving point collocation and the Rayleigh hypothesis
IEEE Transactions on Antennas and Propagation, 1996Summary: It is shown that the Rayleigh hypothesis does not govern convergence of the simple point collocation approach to the numerical solution of scattering by a sinusoidal grating. A recently developed numerical technique, interval arithmetic, is employed to perform some decisive numerical experiments which not only support but guarantee the ...
Christiansen, Søren, Kleinman, Ralph E.
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An isogeometric collocation method using superconvergent points
Computer Methods in Applied Mechanics and Engineering, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anitescu, Cosmin +3 more
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Collocation by L-Splines at Transformed Gaussian Points
SIAM Journal on Numerical Analysis, 1984zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Nonoverlapping domain decomposition with cross points for orthogonal spline collocation
Journal of Numerical Mathematics, 2008A nonoverlapping domain decomposition approach with uniform and matching grids is used to define and compute the orthogonal spline collocation solution of the Dirichlet boundary-value problem for Poisson's equation on a square partitioned into four squares.
Bernard Bialecki, Maksymilian Dryja
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A pseudospectral method for optimal control based on collocation at the Gauss points
2018 IEEE Conference on Decision and Control (CDC), 2018A Gauss collocation method is developed for solving optimal control problems with convex control constraints. The method has a local exponential convergence rate when the solution of the continuous problem is smooth and the Hamiltonian possesses a convexity property.
William W. Hager +4 more
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Maximum principle and convergence analysis for the meshfree point collocation method
SIAM Journal on Numerical Analysis, 2006The discrete Laplacian operator is considered in the sense of the meshfree point collocation method which will be called the strong meshfree Laplacian operator. To define the strong meshfree Laplacian operator, we use the fast version of the generalized moving least square approximation, which can calculate the approximated derivatives of shape ...
Do Wan Kim, Wing Kam Liu
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