What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Partial differential equation
- Numerical analysis
John N. Shadid mostly deals with Applied mathematics, Finite element method, Mathematical analysis, Navier–Stokes equations and Nonlinear system.
His work carried out in the field of Applied mathematics brings together such families of science as Quadrilateral, Euler equations, Geometry, Preconditioner and Discretization.
He focuses mostly in the field of Finite element method, narrowing it down to matters related to Mathematical optimization and, in some cases, System of linear equations.
John N. Shadid has included themes like Mass matrix and Galerkin method in his Mathematical analysis study.
His Navier–Stokes equations study which covers Newton's method that intersects with Computational fluid dynamics, Algebraic equation and Fluid dynamics.
Many of his studies involve connections with topics such as Partial differential equation and Nonlinear system.
His most cited work include:
- Multiphysics simulations: Challenges and opportunities (193 citations)
- Block Preconditioners Based on Approximate Commutators (129 citations)
- Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data (121 citations)
What are the main themes of his work throughout his whole career to date?
His primary areas of study are Applied mathematics, Finite element method, Discretization, Nonlinear system and Mathematical optimization.
His research in Applied mathematics intersects with topics in Domain decomposition methods, Magnetohydrodynamics, Preconditioner, Multigrid method and Navier–Stokes equations.
He studied Preconditioner and Generalized minimal residual method that intersect with System of linear equations.
His Finite element method research incorporates themes from Piecewise linear function, Mathematical analysis, Mechanics and Solver.
His work deals with themes such as Linear system, Euler equations, Algebraic number, Classical mechanics and Fluid dynamics, which intersect with Discretization.
The study incorporates disciplines such as Computational fluid dynamics, Partial differential equation and Runge–Kutta methods in addition to Nonlinear system.
He most often published in these fields:
- Applied mathematics (55.21%)
- Finite element method (52.76%)
- Discretization (37.42%)
What were the highlights of his more recent work (between 2017-2021)?
- Applied mathematics (55.21%)
- Finite element method (52.76%)
- Discretization (37.42%)
In recent papers he was focusing on the following fields of study:
John N. Shadid mainly focuses on Applied mathematics, Finite element method, Discretization, Multigrid method and Preconditioner.
The Applied mathematics study combines topics in areas such as Discontinuous Galerkin method, Conservation law, Magnetohydrodynamics and Nonlinear system.
His Finite element method study combines topics in areas such as Piecewise linear function, Mechanics and Matrix.
His Discretization study integrates concerns from other disciplines, such as Order, Runge–Kutta methods, Nonlinear stability, Fluid dynamics and Plasma modeling.
His Multigrid method study deals with Linear system intersecting with Computational science.
His work investigates the relationship between Preconditioner and topics such as Generalized minimal residual method that intersect with problems in Schur complement.
Between 2017 and 2021, his most popular works were:
- Performance of fully-coupled algebraic multigrid preconditioners for large-scale VMS resistive MHD (10 citations)
- Performance of fully-coupled algebraic multigrid preconditioners for large-scale VMS resistive MHD (10 citations)
- Matrix-free subcell residual distribution for Bernstein finite elements: Monolithic limiting (9 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Partial differential equation
- Numerical analysis
John N. Shadid spends much of his time researching Applied mathematics, Finite element method, Numerical analysis, Multigrid method and Preconditioner.
His Applied mathematics research includes elements of Discretization, Backward Euler method, Euler system, Nonlinear system and Conservation law.
The concepts of his Nonlinear system study are interwoven with issues in Second derivative, Matrix, Convergence, Algebraic number and Smoothness.
John N. Shadid studies Discontinuous Galerkin method which is a part of Finite element method.
John N. Shadid combines subjects such as Variational analysis, Linear system, Krylov subspace, Magnetohydrodynamic generator and Computational science with his study of Numerical analysis.
His biological study spans a wide range of topics, including Nested dissection, Solver, Domain decomposition methods and Benchmark.
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