摘要
针对三维无界区域带有凸多边形导体的瞬时涡流问题,本文提出了一种基于势场的有限元-边界元耦合的方法,从理论上讨论了其能量模误差估计.虽然电场被分解为电矢势A与磁标势φ的梯度之和后增加了方程与未知量的个数,但这种分解可以很好地处理不同介质间的间断.与传统的A-φ法不同,本文讨论了一种全离散的A-φ解耦形式,这样不仅可以避免传统格式所产生的鞍点问题的求解,又可以减少计算量.
This paper is devoted to the study of a FEM-BEM-coupling A-φ method to solve a transient eddy current problem in a 3D unbounded domain with a bounded convex conducting polyhedron. In order to utilize nodal finite elements in space discretization, we decompose the electric field into summation of a vector electric potential and the gradient of a scalar magnetic potential. Although introducing the potentials increases the number of unknowns and equations, these apparent complications are justified by a better way of dealing with pos- sible discontinuities of mediums. As distinguished from the traditional fully-discrete coupled method with both vector and scalar potentials solved in one equation system at every time- step, our decoupled method is to solve them at two separate equation systems, which avoids solving a saddle-point equation system and leads to an important saving in computational effort. The energy-norm error estimate of our method is obtained.
出处
《计算数学》
CSCD
北大核心
2014年第2期163-178,共16页
Mathematica Numerica Sinica
基金
国家自然科学基金(批准号91130015)资助
