We present and analyze a general algorithm which computes an efficient static scheduling of block computations for a parallel $LDL^t$ factorization of sparse symmetric positive definite systems based on a combination of 1D and 2D block distributions. Our solver uses a supernodal fan-in approach and is fully driven by this scheduling. We give an overview of the algorithm and present performance results and comparisons with PSPASES on an IBM-SP2 with 120 MHz Power2SC nodes for a collection of irregular problems.