Abstract interpretation is a general framework for expressing static program analyses. It reduces the problem of extracting properties of a program to computing an approximation of the least fixpoint of a system of equations. The de facto approach for computing an approximation of this fixpoint uses a sequential algorithm based on weak topological order (WTO). This paper presents a deterministic parallel algorithm for fixpoint computation by introducing the notion of weak partial order (WPO). We present an algorithm for constructing a WPO in almost-linear time. Finally, we describe PIKOS, our deterministic parallel abstract interpreter, which extends the sequential abstract interpreter IKOS. We evaluate the performance and scalability of PIKOS on a suite of 1017 C programs. When using 4 cores, PIKOS achieves an average speedup of 2.06x over IKOS, with a maximum speedup of 3.63x. When using 16 cores, PIKOS achieves a maximum speedup of 10.97x.