An efficient parallel implementation of the MSPAI preconditioner

We present an efficient implementation of the Modified SParse Approximate Inverse (MSPAI) preconditioner. MSPAI generalizes the class of preconditioners based on Frobenius norm minimizations, the class of modified preconditioners such as MILU, as well as interface probing techniques in domain decomposition: it adds probing constraints to the basic SPAI formulation, and one can thus optimize the preconditioner relative to certain subspaces. We demonstrate MSPAI's qualities for iterative regularization problems arising from image deblurring. Such applications demand for a fast and parallel preconditioner realization. We present such an implementation introducing two new optimization techniques: First, we avoid redundant calculations using a dictionary. Second, our implementation reduces the runtime spent on the most demanding numerical parts as the code switches to sparse QR decomposition methods wherever profitable. The optimized code runs in parallel with a dynamic load balancing.