有界区域上Helmholtz方程反点源定位
Inverse point source location with the Helmholtz equation on a bounded domain
摘要：
解决了从有限数量的频率处的相应声压的逐点测量中恢复声源，更具体地是单极子的问题。为此目的，考虑一族在测度空间中与有界区域上的Helmholtz方程相结合的稀疏最优化问题。该公式中引入了观测点附近权重无界的加权范数。讨论了在小噪声情况下的最优性条件和恢复条件，从而给出了权值的具体选择。数值实现是基于加速条件梯度法在测度空间和有限元离散。
英文摘要：
The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization problems in measure space in combination with the Helmholtz equation on a bounded domain is considered. A weighted norm with unbounded weight near the observation points is incorporated into the formulation. Optimality conditions and conditions for recovery in the small noise case are discussed, which motivates concrete choices of the weight. The numerical realization is based on an accelerated conditional gradient method in measure space and a finite element discretization.
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