45 citations · 161 across the 19 of their papers we have counts for
20 papers
Robust Discontinuity Indicators for High-Order Reconstruction of Piecewise Smooth Functions
Yipeng Li, Qiao Chen, Xiangmin Jiao
In many applications, piecewise continuous functions are commonly interpolated over meshes. However, accurate high-order manipulations of such functions can be challenging due to p…
Preserving Superconvergence of Spectral Elements for Curved Domains via and -Geometric Refinement
Jacob Jones, Rebecca Conley, Xiangmin Jiao
Spectral element methods (SEM), which are extensions of finite element methods (FEM), are important emerging techniques for solving partial differential equations in physics and en…
Optimal Solutions of Well-Posed Linear Systems via Low-Precision Right-Preconditioned GMRES with Forward and Backward Stabilization
Xiangmin Jiao
Linear systems in applications are typically well-posed, and yet the coefficient matrices may be nearly singular in that the condition number may be close to $1…
ARPIST: Provably Accurate and Stable Numerical Integration over Spherical Triangles
Yipeng Li, Xiangmin Jiao
Numerical integration on spheres, including the computation of the areas of spherical triangles, is a core computation in geomathematics. The commonly used techniques sometimes suf…
HIFIR: Hybrid Incomplete Factorization with Iterative Refinement for Preconditioning Ill-conditioned and Singular Systems
Qiao Chen, Xiangmin Jiao
We introduce a software package called HIFIR for preconditioning sparse, unsymmetric, ill-conditioned, and potentially singular systems. HIFIR computes a hybrid incomplete factoriz…
Optimal and Low-Memory Near-Optimal Preconditioning of Fully Implicit Runge-Kutta Schemes for Parabolic PDEs
Xiangmin Jiao, Xuebin Wang, Qiao Chen
Runge-Kutta (RK) schemes, especially Gauss-Legendre and some other fully implicit RK (FIRK) schemes, are desirable for the time integration of parabolic partial differential equati…
Robust and Efficient Multilevel-ILU Preconditioning of Hybrid Newton-GMRES for Incompressible Navier-Stokes Equations
Qiao Chen, Xiangmin Jiao, Oliver Yang
We introduce a robust and efficient preconditioner for a hybrid Newton-GMRES method for solving the nonlinear systems arising from incompressible Navier-Stokes equations. When the…
Approximate Generalized Inverses with Iterative Refinement for -Accurate Preconditioning of Singular Systems
Xiangmin Jiao, Qiao Chen
We introduce a new class of preconditioners to enable flexible GMRES to find a least-squares solution, and potentially the pseudoinverse solution, of large-scale sparse, asymmetric…
WLS-ENO Remap: Superconvergent and Non-Oscillatory Weighted Least Squares Data Transfer on Surfaces
Yipeng Li, Qiao Chen, Xuebin Wang +1
Data remap between non-matching meshes is a critical step in multiphysics coupling using a partitioned approach. The data fields being transferred often have jumps in function valu…
HILUCSI: Simple, Robust, and Fast Multilevel ILU for Large-Scale Saddle-Point Problems from PDEs
Qiao Chen, Aditi Ghai, Xiangmin Jiao
Incomplete factorization is a widely used preconditioning technique for Krylov subspace methods for solving large-scale sparse linear systems. Its multilevel variants, such as ILUP…
Compact Feature-Aware Hermite-Style High-Order Surface Reconstruction
Yipeng Li, Xinglin Zhao, Navamita Ray +1
High-order surface reconstruction is an important technique for CAD-free, mesh-based geometric and physical modeling, and for high-order numerical methods for solving partial diffe…
Robust Optimal-Complexity Multilevel ILU for Predominantly Symmetric Systems
Aditi Ghai, Xiangmin Jiao
Incomplete factorization is a powerful preconditioner for Krylov subspace methods for solving large-scale sparse linear systems. Existing incomplete factorization techniques, inclu…
A Comparison of Preconditioned Krylov Subspace Methods for Large-Scale Nonsymmetric Linear Systems
Aditi Ghai, Cao Lu, Xiangmin Jiao
Preconditioned Krylov subspace (KSP) methods are widely used for solving large-scale sparse linear systems arising from numerical solutions of partial differential equations (PDEs)…
AP-Cloud: Adaptive Particle-in-Cloud Method for Optimal Solutions to Vlasov-Poisson Equation
Xingyu Wang, Roman Samulyak, Xiangmin Jiao +1
We propose a new adaptive Particle-in-Cloud (AP-Cloud) method for obtaining optimal numerical solutions to the Vlasov-Poisson equation. Unlike the traditional particle-in-cell (PIC…
WLS-ENO: Weighted-Least-Squares Based Essentially Non-Oscillatory Schemes for Finite Volume Methods on Unstructured Meshes
Hongxu Liu, Xiangmin Jiao
ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes are widely used high-order schemes for solving partial differential equations (PDEs), espe…
A Hybrid Method and Unified Analysis of Generalized Finite Differences and Lagrange Finite Elements
Rebecca Conley, Xiangmin Jiao, Tristan J. Delaney
Finite differences, finite elements, and their generalizations are widely used for solving partial differential equations, and their high-order variants have respective advantages…
OPINS: An Orthogonally Projected Implicit Null-space Method for Singular and Nonsingular Saddle-point Systems
Cao Lu, Tristan Delaney, Xiangmin Jiao
Saddle-point systems appear in many scientific and engineering applications. The systems can be sparse, symmetric or nonsymmetric, and possibly singular. In many of these applicati…
Overcoming Element Quality Dependence of Finite Elements with Adaptive Extended Stencil FEM (AES-FEM)
Rebecca Conley, Tristan J. Delaney, Xiangmin Jiao
The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability…
An Embedded Boundary Method for Two Phase Incompressible Flow
Shuqiang Wang, James Glimm, Roman Samulyak +2
We develop an embedded boundary method (EBM) to solve the two-phase incompressible flow with piecewise constant density. The front tracking method is used to track the interface. T…
Consistent Computation of First- and Second-Order Differential Quantities for Surface Meshes
Xiangmin Jiao, Hongyuan Zha
Differential quantities, including normals, curvatures, principal directions, and associated matrices, play a fundamental role in geometric processing and physics-based modeling. C…