What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Numerical analysis
- Algebra
Jinchao Xu mainly focuses on Finite element method, Mathematical analysis, Applied mathematics, Numerical analysis and Multigrid method.
Jinchao Xu interconnects Discretization, Quadratic equation, Basis function and Boundary value problem in the investigation of issues within Finite element method.
His Discretization research incorporates themes from Elliptic curve and Nonlinear system.
His Mathematical analysis study combines topics in areas such as Mixed finite element method, Galerkin method and Divide-and-conquer eigenvalue algorithm.
His studies in Applied mathematics integrate themes in fields like Geometry, Mathematical optimization, Hilbert space and Numerical stability.
His Multigrid method research incorporates elements of Domain decomposition methods and Preconditioner.
His most cited work include:
- Iterative methods by space decomposition and subspace correction (930 citations)
- Parallel multilevel preconditioners (533 citations)
- Two-grid Discretization Techniques for Linear and Nonlinear PDEs (486 citations)
What are the main themes of his work throughout his whole career to date?
Finite element method, Applied mathematics, Mathematical analysis, Multigrid method and Discretization are his primary areas of study.
His Finite element method study combines topics from a wide range of disciplines, such as Grid, Numerical analysis, Boundary value problem and Nonlinear system.
His Applied mathematics research integrates issues from Linear system, Galerkin method, Iterative method, Mathematical optimization and Bounded function.
The various areas that Jinchao Xu examines in his Iterative method study include Subspace topology and Domain decomposition methods.
His work on Curl, Differential equation and Domain as part of his general Mathematical analysis study is frequently connected to Magnetohydrodynamics, thereby bridging the divide between different branches of science.
Jinchao Xu combines subjects such as Conjugate gradient method, Rate of convergence, Smoothing and Preconditioner with his study of Multigrid method.
He most often published in these fields:
- Finite element method (48.43%)
- Applied mathematics (38.33%)
- Mathematical analysis (31.71%)
What were the highlights of his more recent work (between 2018-2021)?
- Applied mathematics (38.33%)
- Finite element method (48.43%)
- Discretization (23.69%)
In recent papers he was focusing on the following fields of study:
Jinchao Xu spends much of his time researching Applied mathematics, Finite element method, Discretization, Artificial neural network and Discontinuous Galerkin method.
Jinchao Xu has researched Applied mathematics in several fields, including Linear system, Preconditioner, Regular polygon, Bounded function and Numerical analysis.
His biological study spans a wide range of topics, including Mathematical analysis, Differential form, Pure mathematics, Representation and Nonlinear system.
Jinchao Xu has included themes like Mixed finite element method, Mechanics, Compressibility, Stability and Numerical tests in his Discretization study.
His Discontinuous Galerkin method research also works with subjects such as
- Galerkin method which intersects with area such as Limit, Element, Elliptic curve, Boundary and Finite element exterior calculus,
- Order that intertwine with fields like Degree,
- Linear elasticity that intertwine with fields like Displacement.
Multigrid method is a subfield of Partial differential equation that Jinchao Xu explores.
Between 2018 and 2021, his most popular works were:
- On the stability and accuracy of partially and fully implicit schemes for phase field modeling (37 citations)
- A unified study of continuous and discontinuous Galerkin methods (27 citations)
- MgNet: A unified framework of multigrid and convolutional neural network (25 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Algebra
- Geometry
Applied mathematics, Finite element method, Artificial neural network, Activation function and Discontinuous Galerkin method are his primary areas of study.
His research in Applied mathematics intersects with topics in Numerical analysis and Piecewise.
Jinchao Xu studies Linear elasticity which is a part of Finite element method.
His Artificial neural network research is multidisciplinary, incorporating perspectives in Class, Multigrid method, Polynomial and Convolutional neural network.
In his study, Special case, Basis function, Representation, Piecewise linear function and Numerical partial differential equations is strongly linked to Function, which falls under the umbrella field of Activation function.
His studies deal with areas such as Galerkin method and Mathematical analysis, Limit as well as Discontinuous Galerkin method.
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