What is he best known for?
The fields of study he is best known for:
- Quantum mechanics
- Mathematical analysis
- Geometry
His scientific interests lie mostly in Discontinuous Galerkin method, Finite volume method, Applied mathematics, Mathematical analysis and Finite element method.
Michael Dumbser combines subjects such as Polynomial, Basis function, Conservation law, Numerical analysis and Piecewise with his study of Discontinuous Galerkin method.
His study looks at the relationship between Numerical analysis and fields such as Geometry, as well as how they intersect with chemical problems.
The concepts of his Finite volume method study are interwoven with issues in Nonlinear system, Partial differential equation, Taylor series and Euler equations.
The study incorporates disciplines such as Galerkin method, Mathematical optimization, Order of accuracy, Euler's formula and Discretization in addition to Applied mathematics.
Michael Dumbser has researched Mathematical optimization in several fields, including Polygon mesh and Adaptive mesh refinement.
His most cited work include:
- A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes (412 citations)
- Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems (344 citations)
- An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes – II. The three-dimensional isotropic case (329 citations)
What are the main themes of his work throughout his whole career to date?
Michael Dumbser spends much of his time researching Finite volume method, Discontinuous Galerkin method, Applied mathematics, Mathematical analysis and Discretization.
His Finite volume method research is multidisciplinary, relying on both Polygon mesh, Galerkin method, Nonlinear system, Numerical analysis and Piecewise.
Discontinuous Galerkin method is a subfield of Finite element method that Michael Dumbser studies.
His Applied mathematics research integrates issues from Euler equations, Hyperbolic partial differential equation, Partial differential equation, Mathematical optimization and Conservation law.
His Mathematical analysis research is multidisciplinary, incorporating perspectives in Compressibility and Riemann solver.
His Discretization research incorporates elements of Linear system, Finite difference, Shallow water equations, Conjugate gradient method and Computation.
He most often published in these fields:
- Finite volume method (54.09%)
- Discontinuous Galerkin method (55.64%)
- Applied mathematics (47.47%)
What were the highlights of his more recent work (between 2019-2021)?
- Discontinuous Galerkin method (55.64%)
- Applied mathematics (47.47%)
- Nonlinear system (21.01%)
In recent papers he was focusing on the following fields of study:
His primary areas of investigation include Discontinuous Galerkin method, Applied mathematics, Nonlinear system, Finite volume method and Hyperbolic partial differential equation.
His Discontinuous Galerkin method research is classified as research in Finite element method.
His Applied mathematics research incorporates themes from Partial differential equation, Curl, Eulerian path, Conservation law and Piecewise.
His Nonlinear system study combines topics in areas such as Discretization, Mathematical analysis, Wave propagation, Linear elasticity and Mechanics.
His studies deal with areas such as Nonlinear Schrödinger equation, Schrödinger equation, Compressibility and Continuum mechanics as well as Finite volume method.
The various areas that Michael Dumbser examines in his Hyperbolic partial differential equation study include General relativity, Polygon mesh, Polynomial and Computational science.
Between 2019 and 2021, his most popular works were:
- High order ADER schemes for continuum mechanics (31 citations)
- ExaHyPE : an engine for parallel dynamically adaptive simulations of wave problems. (25 citations)
- High order direct Arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes (24 citations)
In his most recent research, the most cited papers focused on:
- Quantum mechanics
- Mathematical analysis
- Geometry
Michael Dumbser mainly investigates Hyperbolic partial differential equation, Finite volume method, Discontinuous Galerkin method, Applied mathematics and Conservation law.
His Hyperbolic partial differential equation research includes themes of General relativity, Biot number, Mechanics, Compressible flow and Longitudinal wave.
Michael Dumbser combines subjects such as Polygon mesh, Mathematical analysis, Compressibility and Continuum mechanics with his study of Finite volume method.
Michael Dumbser interconnects Discretization, Finite element method and Inviscid flow in the investigation of issues within Compressibility.
His Applied mathematics research is multidisciplinary, incorporating elements of Eulerian path, Curl and Scalar.
His work deals with themes such as Voronoi diagram and Generator, Topology, which intersect with Conservation law.
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