Wilkinson defined a sparse matrix as one with enough zeros that it pays to take advantage of
them. 1 This informal yet practical definition captures the essence of the goal of direct …

In this chapter we will give an insight into the development of modern sparse elimination
methods. These are driven by a preprocessing phase based on combinatorial algorithms …

Power flow analysis is critical for power systems due to the development of multiple energy
supplies. For safety, stability, and real-time response in grid operation, grid planning, and …

Sparse direct solvers play a vital role in large-scale high performance computing in science
and engineering. Existing distributed sparse direct methods employ multifrontal/supernodal …

Static timing analysis (STA) in advanced technology nodes encounter many new challenges
in analysis accuracy and speed efficiency. To accurately model complex interconnect …

Lower upper (LU) factorization for sparse matrices is the most important computing step for
circuit simulation problems. However, parallelizing LU factorization on the graphic …

Editor's note: Many scientific computing problems, including circuit simulations, rely on
efficient lower-upper (LU) decomposition of sparse matrices. Prior studies took advantage of …

To analyze large sets of grid states, eg when evaluating the impact from the uncertainties of
the renewable generation with probabilistic Monte Carlo simulation or in stationary time …

Sparse LU factorization is one of the key building blocks of sparse direct solvers and often
dominates the computing time of circuit simulation programs. Existing GPU-accelerated …

This letter proposes a superior GPU-accelerated algorithm for probabilistic power flow (PPF)
based on Monte-Carlo simulation with simple random sampling (MCS-SRS). By means of …