Summary
International Symposium on Nonlinear Theory and its Applications
2010
Session Number:C1L-D
Session:
Number:C1L-D2
Comparison of the linear algebra approach and the evolutionary computing for magnetic field shaping in linear coils.
Bart?omiej Garda, Zbigniew Galias,
pp.508-511
Publication Date:2010/9/5
Online ISSN:2188-5079
Summary:
In this work we consider the problem of shaping magnetic field excited by magnetic coils. An important special case is constructing coils that excite a homogenous magnetic field in some specific regions. This problem is an important step in the design of superconducting magnetic coils for Magnetic Resonance Imaging devices, where in certain regions a strong static magnetic field with high homogeneity is needed. In this work, the authors investigate the problem of a linear coil design using two approaches. The first approach is based on linear algebra. The problem under study can be formulated as an over-determined set of linear equations. Since usually the matrix A describing the problem is illconditioned, solutions obtained using the standard method of least squares are very large in magnitude and hence are useless from the applications point of view. Therefore, a regularization method is employed to make the linear problem well-posed. The second method considered uses evolutionary computations. These two techniques are compared in terms of effectiveness and computational complexity. Performance of both methods is evaluated using several examples.