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Title of Journal: Numer Algor

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Abbravation: Numerical Algorithms

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Springer US

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DOI

10.1007/s00715-014-0359-9

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1572-9265

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The impact of parameter selection on the performan

Authors: Peter K Moore
Publish Date: 2007/11/09
Volume: 46, Issue: 2, Pages: 121-139
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Abstract

The performance of automatic codes for solving reaction–diffusion systems is controlled by a variety of parameters Some of them are invisible to the user while others can be modified For the latter default values are available The effects of four such parameters are studied for a code that couples the methodoflines in time with a highorder hrefinement finite element strategy in space The key parameters considered are the ratio of the temporal error tolerance to the spatial error tolerance two parameters governing convergence of the iterative methods for the linear and nonlinear systems and the number of time steps between regridding These parameters are typical in methodoflines based codes Computations on a model problem demonstrate that both small and large temporal to spatial error ratios lead to performance degradation as does less frequent regridding They also show that insufficient convergence in the nonlinear solver can reduce the reliability of the spatial error estimates

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  1. Correction of eigenvalues estimated by the Legendre–Gauss Tau method
  2. Design with L-splines
  3. Accelerated Landweber methods based on co-dilated orthogonal polynomials
  4. A small note on the scaling of symmetric positive definite semiseparable matrices
  5. Solitary wave solutions of the one-dimensional Boussinesq equations
  6. Numerical solutions of index-1 differential algebraic equations can be computed in polynomial time
  7. Recursive self preconditioning method based on Schur complement for Toeplitz matrices
  8. A subspace conjugate gradient algorithm for large-scale unconstrained optimization
  9. The sparse cardinal sine decomposition and its application for fast numerical convolution
  10. A family of Steffensen type methods with seventh-order convergence
  11. On linearly related orthogonal polynomials in several variables
  12. Orthogonal polynomials—centroid of their zeroes
  13. Numerical methods for computing sensitivities for ODEs and DDEs
  14. A new subtraction-free formula for lower bounds of the minimal singular value of an upper bidiagonal matrix
  15. Extrapolation algorithms for solving nonlinear boundary integral equations by mechanical quadrature methods
  16. A global convergent derivative-free method for solving a system of non-linear equations
  17. A new constrained total variational deblurring model and its fast algorithm
  18. Numerical solution to generalized Lyapunov/Stein and rational Riccati equations in stochastic control
  19. Tracing the Pareto frontier in bi-objective optimization problems by ODE techniques
  20. A study of accelerated Newton methods for multiple polynomial roots
  21. A binary powering Schur algorithm for computing primary matrix roots
  22. Non-uniform exponential tension splines
  23. Nonmonotone line search methods with variable sample size
  24. Galerkin-Chebyshev spectral method and block boundary value methods for two-dimensional semilinear parabolic equations
  25. On approximated ILU and UGS preconditioning methods for linearized discretized steady incompressible Navier-Stokes equations
  26. Accelerated hybrid conjugate gradient algorithm with modified secant condition for unconstrained optimization
  27. A marching-on in time meshless kernel based solver for full-wave electromagnetic simulation
  28. Algorithms and software for total variation image reconstruction via first-order methods
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