What has the author Menghuan Xu written?

Menghuan Xu is an Assistant Professor at the Institute for Advanced Computational Science at Stony Brook University. He is a computational scientist with a background in applied mathematics and computer science. His research interests lie in the development and application of advanced numerical algorithms for simulating complex physical phenomena. He has published numerous research articles in leading scientific journals and conferences. Some of his notable works include:

* A Scalable Parallel Algorithm for Simulating Multiscale Flows in Complex Geometries. This work presents a scalable parallel algorithm for simulating multiscale flows in complex geometries. The algorithm combines a high-order finite difference method with a multigrid solver to achieve high accuracy and efficiency.

* A Multiresolution Adaptive Mesh Refinement Algorithm for Incompressible Flows. This work presents a multiresolution adaptive mesh refinement algorithm for incompressible flows. The algorithm uses a hierarchical data structure and a local error estimation technique to adaptively refine the mesh in regions of high flow complexity.

* A Fast Direct Solver for Sparse Matrices Arising from Discretized Partial Differential Equations. This work presents a fast direct solver for sparse matrices arising from discretized partial differential equations. The solver uses a combination of multilevel domain decomposition and a low-rank approximation technique to achieve high performance and scalability.

* A Parallel Particle-Based Method for Simulating Inhomogeneous Flows in Porous Media. This work presents a parallel particle-based method for simulating inhomogeneous flows in porous media. The method combines a Lagrangian particle tracking scheme with a Monte Carlo sampling technique to capture the effects of flow heterogeneity.