Martin Weiser

Adaptation of antenna profiles for control of MR guided hyperthermia (HT) in a hybrid MR‐HT system

A combined numerical-experimental iterative procedure, based on the Gauss-Newton algorithm, has been developed for control of magnetic resonance (MR)-guided hyperthermia (HT) applications in a hybrid MR-HT system BSD 2000 3D-MRI. In this MR-HT system, composed of a 3-D HT applicator Sigma-Eye placed inside a tunnel-type MR tomograph Siemens MAGNETOM Symphony (1.5 T), the temperature rise due to the HT radiation can be measured on-line in three dimensions by use of the proton resonance frequency shift (PRFS) method. The basic idea of our iterative procedure is the improvement of the systems characterization by a step-by-step modification of the theoretical HT antenna profiles (electric fields radiated by single antennas). The adaptation of antenna profiles is efficient if the initial estimates are radiation fields calculated from a good a priori electromagnetic model. Throughout the iterative procedure, the calculated antenna fields (FDTD) are step-by-step modified by comparing the calculated and experimental data, the latter obtained using the PRFS method. The procedure has been experimentally tested on homogeneous and inhomogeneous phantoms. It is shown that only few comparison steps are necessary for obtaining a dramatic improvement of the general predictability and quality of the specific absorption rate (SAR) inside the MR-HT hybrid system.

Affine conjugate adaptive Newton methods for nonlinear elastomechanics

The paper extends affine conjugate Newton methods from convex to nonconvex minimization, with particular emphasis on PDE problems originating from compressible hyperelasticity. On the basis of well-known schemes from finite dimensional nonlinear optimization, three different algorithmic variants are worked out in a function space setting, which permits an adaptive multilevel finite element implementation. These algorithms are tested on two well-known 3D test problems and a real-life example from surgical operation planning.

Global Inexact Newton Multilevel FEM for Nonlinear Elliptic Problems

The paper deals with the multilevel solution of elliptic partial differential equations (PDEs) in a finite element setting: uniform ellipticity of the PDE then goes with strict monotonicity of the derivative of a nonlinear convex functional. A Newton multigrid method is advocated, wherein linear residuals are evaluated within the multigrid method for the computation of the Newton corrections. The globalization is performed by some damping of the ordinary Newton corrections. The convergence results and the algorithm may be regarded as an extension of those for local Newton methods presented recently by the authors. An affine conjugate global convergence theory is given, which covers both the exact Newton method (neglecting the occurrence of approximation errors) and inexact Newton-Galerkin methods addressing the crucial issue of accuracy matching between discretization and iteration errors. The obtained theoretical results are directly applied for the construction of adaptive algorithms. Finally, illustrative numerical experiments with a NEWTON-KASKADE code are documented.

Inertia-Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization

Fast nonlinear programming methods following the all-at-once approach usually employ Newtons method for solving linearized Karush-Kuhn-Tucker (KKT) systems. In nonconvex problems, the Newton direction is guaranteed to be a descent direction only if the Hessian of the Lagrange function is positive definite on the nullspace of the active constraints; otherwise some modifications to Newtons method are necessary. This condition can be verified using the signs of the KKT eigenvalues (inertia), which are usually available from direct solvers for the arising linear saddle point problems. Iterative solvers are mandatory for very large-scale problems, but in general they do not provide the inertia. Here we present a preconditioner based on a multilevel incomplete

The convergence of an interior point method for an elliptic control problem with mixed control-state constraints

LBL^T

Interior Point Methods in Function Space

factorization, from which an approximation of the inertia can be obtained. The suitability of the heuristics for application in optimization methods is verified on an interior point method applied to the CUTE and COPS test problems, on large-scale three-dimensional (3D) PDE-constrained optimal control problems, and on 3D PDE-constrained optimization in biomedical cancer hyperthermia treatment planning. The efficiency of the preconditioner is demonstrated on convex and nonconvex problems with

Fully adaptive propagation of the quantum-classical Liouville equation

150^3

Asymptotic Mesh Independence of Newton's Method Revisited

state variables and

Comparison of MR-thermography and planning calculations in phantoms

150^2

Superlinear convergence of the control reduced interior point method for PDE constrained optimization

control variables, both subject to bound constraints.