Penalty algorithm adapted for the spectral element discretization of the Darcy equations

Any spectral element discretization of the Darcy problem can be efficiently solved by applying the penalty method. This method leads to a system of equations with uncoupled unknowns. We prove a posteriori error estimates for a spectral element discretization of the Darcy problem. The proposed algorithm permits the optimization of the penalty parameter as a function of the error indicators.

Weighted Block Sparse Recovery Algorithm for High Resolution DOA Estimation with Unknown Mutual Coupling

Based on weighted block sparse recovery, a high resolution direction-of-arrival (DOA) estimation algorithm is proposed for data with unknown mutual coupling. In our proposed method, a new block representation model based on the array covariance vectors is firstly formulated to avoid the influence of unknown mutual coupling by utilizing the inherent structure of the steering vector. Then a weighted 1l -norm penalty algorithm is proposed to recover the block sparse matrix, in which the weighted matrix is constructed based on the principle of a novel Capon space spectrum function for increasing the sparsity of solution. Finally, the DOAs can be obtained from the position of the non-zero blocks of the recovered sparse matrix. Due to the use of the whole received data of array and the enhanced sparsity of solution, the proposed method effectively avoids the loss of the array aperture to achieve a better estimation performance in the environment of unknown mutual coupling in terms of both spatial resolution and accuracy. Simulation experiments show the proposed method achieves better performance than other existing algorithms to minimize the effects of unknown mutual coupling.