We describe an optimization process specially designed for regional hyperthermia of deep-seated tumors in order to achieve desired steady-state temperature distributions. A nonlinear three-dimensional heat transfer model based on temperature-dependent blood perfusion is applied predict the temperature. Using linearly implicit methods time and adaptive multilevel finite elements space, we are able integrate efficiently instationary equation with high accuracy. Optimal heating obtained by...

The paper introduces and studies numerical methods that are fully adaptive in both three-dimensional (3D) space time to challenging multiscale cardiac reaction-diffusion models. In these methods, temporal adaptivity comes via stepsize control function oriented linearly implicit integration, while spatial is realized within multilevel finite element controlled by a posteriori local error estimators. contrast other recent approaches modeling discretize first then (so-called method of lines),...

In this paper, we study the problem of technical transient gas network optimization, which can be considered a minimum cost flow with nonlinear objective function and additional constraints on arcs. Applying an implicit box scheme to isothermal Euler equation, derive mixed-integer program. This is solved by means combination (i) novel linear programming approach based piecewise linearization (ii) classical sequential quadratic program applied for given combinatorial constraints. Numerical...

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 unstructured 3-D tetrahedral grids. Spatial discretization done by employing hierarchical -conforming elements proposed Ainsworth and Coyle. For time discretization, we use newly constructed one-step Rosenbrock ROS3PL third order accuracy in time. Adaptive mesh refinement coarsening are based...

Physics informed neural networks have been recently proposed and offer a new promising method to solve differential equations. They adapted many more scenarios different variations of the original proposed. In this case study we review these variations. We focus on variants that can compensate for imbalances in loss function perform comprehensive numerical comparison with application gas transport problems. Our includes formulations function, algorithmic balancing methods, optimization...

SUMMARY This paper is motivated by an optimal boundary control problem for the cooling process of molten and already formed glass down to room temperature. The high temperatures at which processed demand include radiative heat transfer in computational model. Since complete equations are too complex optimization purposes, we use simplified approximations spherical harmonics coupled with a practically relevant frequency bands considered as partial differential algebraic equation...

ABSTRACT: We describe an optimization process specially designed for regional hyperthermia of deep seated tumors in order to achieve desired steady‐state temperature distributions. A nonlinear three‐dimensional heat‐transfer model based on temperature‐dependent blood perfusion is applied predict the temperature. Optimal heating obtained by minimizing integral object function which measures distance between and predicted temperatures. Sequential minima are calculated from successively...

This paper addresses global error estimation and control for initial value problems ordinary differential equations. The focus lies on a comparison between novel approach based the adjoint method combined with small sample statistical initialization classical first variational equation. Control is achieved through tolerance proportionality. Both approaches are found to work well enable in reliable manner.