Weak-form time-domain perfectly matched layer

In near-field wave simulation, it is necessary to truncate the infinite-domain via highly accurate absorbing boundary condition to improve the computational efficiency. Perfectly matched layer is one kind of highly accurate absorbing boundary condition formulated as absorbing layer. In traditional way, the strong-form field equation of PML together with the boundary and/or interface condition of PML are obtained by complex stretching their counterparts in infinite domain. However, the boundary and/or interface condition of infinite domain have also been applied for PML without any modification. The construction of PML's field equation and its boundary and/or interface conditions are independent of each other, the two may be improperly matched, which lead to numerical instability and the deterioration of numerical accuracy. In this paper, a new method for PML derivation is proposed. PML is obtained by complex stretching the weak form wave equation in infinite domain. Since the weak-form wave equation has combined the wave equation and the boundary and/or interface condition, the mismatch between the obtained field equation and boundary and/or interface condition can be naturally avoided. Via the new method, the weak-form time-domain PML can be derived in a straight way, strong-form PML can also be derived. The former is ready for discretization with finite element method, while the latter could be discretized by finite difference method. Applying Legendre spectral element method for space discretization, full scheme for near-field wave simulation in elastic media has been established. The numerical stability and the accuracy of new scheme is illustrated by numerical tests. The method for PML construction can be directly applied for multi-phase media near-field wave simulation.