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Impact of nonlinear heat transfer on temperature control in regional hyperthermia
TLDR
An optimization process specially designed for regional hyperthermia of deep-seated tumors in order to achieve desired steady-state temperature distributions using linearly implicit methods in time and adaptive multilevel finite elements in space is described.
Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems - Theory, Algorithm, and Applications
  • J. Lang
  • Computer Science, Mathematics
    Lecture Notes in Computational Science and…
  • 2001
TLDR
The Rosenbrock Algorithm is an Effective Algorithm for Computational Error Estimation and its Applications are Applications from Computational Sciences.
ROS3P—An Accurate Third-Order Rosenbrock Solver Designed for Parabolic Problems
In this note we present a new Rosenbrock solver which is third-order accurate for nonlinear parabolic problems. Since Rosenbrock methods suffer from order reduction when they are applied to partial
Optimization of Temperature Distributions for Regional Hyperthermia Based on a Nonlinear Heat Transfer Model a
TLDR
An optimization process specially designed for regional hyperthermia of deep seated tumors in order to achieve desired steady‐state temperature distributions based on temperature‐dependent blood perfusion is described.
Towards a Fully Space-Time Adaptive FEM for Magnetoquasistatics
This paper is concerned with fully space-time adaptive magnetic field computations. We describe a Whitney finite element method for solving the magnetoquasistatic formulation of Maxwell's equations
On Global Error Estimation and Control for Initial Value Problems
htmlabstractThis paper addresses global error estimation and control for initial value problems for ordinary differential equations. The focus lies on a comparison between a novel approach based on
Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology
TLDR
The adaptive method accurately resolves the evolution of the intra- and extracellular potentials, gating variables, and ion concentrations during the excitation, plateau, and recovery phases of complex cardiac reaction-diffusion models.
Hierarchical Modelling and Model Adaptivity for Gas Flow on Networks
TLDR
A strategy to adaptively apply the different models in different regions of the network while maintaining the accuracy of the solution is presented.
A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates
TLDR
Numerical results show that a few GS iterations are sufficient for obtaining a reasonably good approximation to the error for use in anisotropic mesh adaptation.
Comparison of the asymptotic stability for multirate Rosenbrock methods
  • K. Kuhn, J. Lang
  • Computer Science, Mathematics
    J. Comput. Appl. Math.
  • 1 May 2014
TLDR
It is given stability regions and illustrated their importance for a two-component test problem and different linearly implicit Rosenbrock methods in a recursive multirate procedure.
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