用类周长罚和相场法重建裂纹和材料损失：数值结果
Reconstruction of cracks and material losses by perimeter-like penalizations and phase-field methods: numerical results
摘要：
我们数值实现的变分方法重建的反裂纹和空腔问题的作者之一。该方法是基于一个适当适应的自由不连续性问题。它的主要特点是使用相场函数来描述要重建的缺陷，并使用类似周长的惩罚来正则化不适定问题。数值实现是基于相应的最优性系统的解决方案的梯度法。通过数值模拟验证了该方法的有效性。
英文摘要：
We numerically implement the variational approach for reconstruction in the inverse crack and cavity problems developed by one of the authors. The method is based on a suitably adapted free-discontinuity problem. Its main features are the use of phase-field functions to describe the defects to be reconstructed and the use of perimeter-like penalizations to regularize the ill-posed problem. The numerical implementation is based on the solution of the corresponding optimality system by a gradient method. Numerical simulations are presented to show the validity of the method.
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