Circuit simulations are essential in the development of new chips. In the simulation, some of which may take up to several weeks, a significant part of the computational effort goes into the solving of a linear system. While there have been advances to optimize the solvers, parallelization still proves to be a difficult task: Due to the irregular structure, the high sparsity and the data dependence in circuit matrices, achieving high levels of parallelization is particularly challenging. As of today, there is still great research potential in parallelizing LU solvers designed for circuit simulations. In this thesis a direct LU solver designed for circuit matrices is developed based on the state-of-the-art solver NICSLU. The solver employs a left-looking LU factorization, which is well suited for parallelization. As the structure of a circuit matrix rarely changes throughout the different factorizations of a simulation, the algorithm is adapted to exploit this particular feature. Furthermore, modern OpenMP programming techniques are used to explore dynamic scheduling strategies, aiming to better handle the irregularity and sparsity of circuit matrices. Finally, the solver will be evaluated both in terms of computing efficiency and numerical accuracy. This thesis aims to provide a highly efficient parallel LU solver tailored for circuit simulations.