What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Geometry
- Partial differential equation
Ralf Hiptmair mainly focuses on Mathematical analysis, Galerkin method, Finite element method, Discretization and Boundary.
His Mathematical analysis research includes elements of Scattering and Plane wave.
His Galerkin method research focuses on Boundary element method and how it connects with Neumann boundary condition.
The various areas that Ralf Hiptmair examines in his Finite element method study include Bilinear form, Differential form and Pure mathematics.
Ralf Hiptmair has included themes like Solenoidal vector field, Multigrid method, Applied mathematics and Maxwell's equations in his Discretization study.
His work in Boundary covers topics such as Integral equation which are related to areas like Polyhedron and Electromagnetic radiation.
His most cited work include:
- Finite elements in computational electromagnetism (670 citations)
- Multigrid Method for Maxwell's Equations (340 citations)
- Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces (212 citations)
What are the main themes of his work throughout his whole career to date?
The scientist’s investigation covers issues in Mathematical analysis, Finite element method, Discretization, Galerkin method and Boundary.
As part of his studies on Mathematical analysis, Ralf Hiptmair often connects relevant areas like Boundary element method.
His Finite element method research integrates issues from Curl, Multigrid method, Applied mathematics, Maxwell's equations and Differential form.
His Discretization research is multidisciplinary, relying on both Bounded function and Tensor product.
His work in Galerkin method tackles topics such as Numerical analysis which are related to areas like Partial differential equation.
His Boundary study which covers Domain that intersects with Piecewise and Polynomial.
He most often published in these fields:
- Mathematical analysis (59.09%)
- Finite element method (30.81%)
- Discretization (26.26%)
What were the highlights of his more recent work (between 2018-2021)?
- Mathematical analysis (59.09%)
- Boundary (21.72%)
- Domain (8.59%)
In recent papers he was focusing on the following fields of study:
His scientific interests lie mostly in Mathematical analysis, Boundary, Domain, Finite element method and Scattering.
His work in Mathematical analysis is not limited to one particular discipline; it also encompasses Boundary element method.
His work carried out in the field of Boundary element method brings together such families of science as Mixed finite element method, Galerkin method and Extended finite element method.
His Boundary research is multidisciplinary, incorporating perspectives in Transmission and Dirichlet distribution.
His Domain study incorporates themes from Bounded function, Lipschitz domain and Pure mathematics.
His studies in Finite element method integrate themes in fields like Classical mechanics and Maxwell's equations.
Between 2018 and 2021, his most popular works were:
- First-Kind Boundary Integral Equations for the Hodge--Helmholtz Operator (6 citations)
- Discrete regular decompositions of tetrahedral discrete 1-forms: Discrete regular decompositions of tetrahedral discrete 1-forms (5 citations)
- Optimal Operator Preconditioning for Galerkin Boundary Element Methods on 3-Dimensional Screens (4 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Geometry
- Partial differential equation
Ralf Hiptmair focuses on Mathematical analysis, Boundary, Maxwell's equations, Operator and Finite element method.
Ralf Hiptmair performs integrative Mathematical analysis and Field research in his work.
His Boundary course of study focuses on Domain and Acoustics, Scattering, Transmission and Representation.
His Maxwell's equations research incorporates themes from Trefftz method, Partial derivative and Boundary integral equations.
The Finite element method study combines topics in areas such as Discretization, Scalar and Applied mathematics.
His Discretization study frequently involves adjacent topics like Boundary value problem.
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