Rainer Kress

Rainer Kress's AcademicInfluence.com Rankings

Rainer Kress

Physics

#4285

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#5911

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physics Degrees

Rainer Kress

Mathematics

#5604

World Rank

#7872

Historical Rank

Applied Mathematics

#153

World Rank

#170

Historical Rank

Measure Theory

#832

World Rank

#1099

Historical Rank

mathematics Degrees

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Mathematics

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Rainer Kress's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Inverse Acoustic and Electromagnetic Scattering Theory (1992) (5179)
Integral equation methods in scattering theory (1983) (2078)
Linear Integral Equations (1989) (1667)
On the numerical solution of a hypersingular integral equation in scattering theory (1995) (222)
Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering (1985) (201)
A Nyström method for boundary integral equations in domains with corners (1990) (201)
Inverse scattering from an open arc (1995) (188)
Uniqueness in inverse obstacle scattering (acoustics) (1993) (178)
Numerical Analysis (1998) (170)
Nonlinear integral equations and the iterative solution for an inverse boundary value problem (2005) (158)
Transmission problems for the Helmholtz equation (1978) (154)
Two methods for solving the inverse acoustic scattering problem (1988) (132)
Using fundamental solutions in inverse scattering (2006) (110)
Boundary integral equations in time-harmonic acoustic scattering (1991) (99)
Inverse scattering for shape and impedance (2001) (95)
Newton’s method for inverse obstacle scattering meets the method of least squares (2003) (94)
On the far‐field operator in elastic obstacle scattering (2002) (94)
UNIQUENESS IN INVERSE OBSTACLE SCATTERING (2002) (93)
Identification of sound-soft 3D obstacles from phaseless data (2010) (87)
On the denseness of Herglotz wave functions and electromagnetic Herglotz pairs in Sobolev spaces (2001) (85)
A quasi-Newton method in inverse obstacle scattering (1994) (83)
On uniqueness in inverse obstacle scattering (1993) (80)
On the condition number of boundary integral operators for the exterior Dirichlet problem for the Helmholtz equation (1983) (80)
On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation (1993) (78)
On the numerical solution of an inverse boundary value problem for the heat equation (1998) (75)
Eigenvalues of the Far Field Operator for the Helmholtz Equation in an Absorbing Medium (1995) (72)
A hybrid method for two-dimensional crack reconstruction (2005) (72)
Integral equations for inverse problems in corrosion detection from partial Cauchy data (2007) (70)
Inverse elastic scattering from a crack (1996) (69)
Inverse Obstacle Scattering with Modulus of the Far Field Pattern as Data (1997) (67)
Inverse scattering for surface impedance from phase-less far field data (2011) (65)
Reconstruction of a current distribution from its magnetic field (2002) (65)
Nonlinear Integral Equations for Solving Inverse Boundary Value Problems for Inclusions and Cracks (2006) (64)
A NUMERICAL METHOD FOR AN INVERSE SCATTERING PROBLEM (1987) (63)
An inverse boundary value problem for the heat equation: the Neumann condition (1999) (60)
Eigenvalues of the far field operator and inverse scattering theory (1995) (59)
On an Integral Equation of the first Kind in Inverse Acoustic Scattering (1986) (58)
Rothe's Method for the Heat Equation and Boundary Integral Equations (1997) (58)
On the Fréchet Derivative for Obstacle Scattering with an Impedance Boundary Condition (2004) (57)
Conformal mappings and inverse boundary value problems (2005) (55)
On the numerical solution of the three-dimensional inverse obstacle scattering problem (1992) (55)
Inverse scattering from an orthotropic medium (1997) (55)
Nonlinear integral equations for the inverse electrical impedance problem (2007) (55)
Integral equation methods for scattering from an impedance crack (2003) (53)
Transmission Eigenvalues (2021) (53)
On the Far Field in Obstacle Scattering (1999) (52)
Inverse Obstacle Scattering Using Reduced Data (1998) (51)
Inverse scattering for a locally perturbed half-plane (2000) (50)
A hybrid method for sound-hard obstacle reconstruction (2007) (48)
On the simulation source technique for exterior problems in acoustics (1986) (48)
Inverse Dirichlet problem and conformal mapping (2004) (48)
Integral equation methods for the inverse obstacle problem with generalized impedance boundary condition (2012) (47)
Direct and inverse scattering problems for inhomogeneous impedance cylinders of arbitrary shape (2003) (46)
CORRIGENDUM: Uniqueness in inverse obstacle scattering with conductive boundary condition (1996) (46)
Huygens’ principle and iterative methods in inverse obstacle scattering (2010) (45)
Electrostatic imaging via conformal mapping (2002) (45)
NONLINEAR INTEGRAL EQUATIONS IN INVERSE OBSTACLE SCATTERING (2006) (43)
Inverse electromagnetic scattering in a two-layered medium with an application to mine detection (2008) (43)
Looking Back on Inverse Scattering Theory (2018) (42)
On the exterior boundary-value problem for the time-harmonic Maxwell equations (1979) (41)
A new algorithm in electromagnetic inverse scattering theory with an application to medical imaging (1997) (37)
Integral equations for shape and impedance reconstruction in corrosion detection (2010) (35)
Iterative reconstruction of dielectric rough surface profiles at fixed frequency (2006) (33)
Fréchet differentiability of the far field operator for scattering from a crack (1995) (33)
The impedance boundary value problem for the time harmonic Maxwell equations (1981) (33)
Uniqueness and numerical methods in inverse obstacle scattering (2007) (33)
On an integral equation for the two-dimensional exterior Stokes problem☆ (1985) (32)
On the numerical solution of a hypersingular integral equation for elastic scattering from a planar crack (2000) (32)
On the limiting behaviour of solutions to boundary integral equations associated with time harmonic wave equations for small frequencies (1979) (31)
A boundary integral equation method for the transmission eigenvalue problem (2017) (30)
Numerical Solution of Boundary Integral Equations in Time-Harmonic Electromagnetic Scattering (1990) (29)
Time harmonic electromagnetic waves in an inhomogeneous medium (1990) (29)
Ill-Posed Problems (2019) (28)
Dense Sets and Far Field Patterns in Electromagnetic Wave Propagation (1985) (28)
On the boundary operator in electromagnetic scattering (1986) (28)
Inverse Scattering (2015) (27)
Integral equation methods in inverse obstacle scattering (2000) (27)
On nonnormal matrices (1974) (27)
Linear sampling methods for inverse boundary value problems in potential theory (2002) (27)
On the Condition Number of Integral Equations in Acoustics using Modified Fundamental Solutions (1983) (27)
On the low wave number asymtotics for the two‐dimensional exterior dirichlet problem for the reduced wave equation (1987) (27)
Iterative and range test methods for an inverse source problem for acoustic waves (2009) (26)
On the General Hermite Cardinal Interpolation (1972) (25)
Inverse scattering for planar cracks via nonlinear integral equations (2008) (24)
On constant-alpha force-free fields in a torus (1986) (20)
On a two-dimensional inverse scattering problem for a dielectric (2012) (19)
A second order Newton method for sound soft inverse obstacle scattering (2009) (19)
Inverse scattering for an impedance cylinder buried in a dielectric cylinder (2009) (19)
On an exterior boundary-value problem for the time-harmonic Maxwell equations with boundary conditions for the normal components of the electric and magnetic field (1986) (19)
A Sinc Quadrature Method for the Double-Layer Integral Equation in Planar Domains with Corners (1998) (18)
An inverse boundary value problem for the Oseen equation (2000) (18)
Far field patterns and inverse scattering problems for imperfectly conducting obstacles (1989) (18)
A remark on a boundary value problem for force-free fields (1977) (18)
The unique solvability of the null field equations of acoustics (1983) (18)
Integral equations for an inverse boundary value problem for the two-dimensional Stokes equations (2007) (18)
UNIQUENESS IN INVERSE OBSTACLE SCATTERING FOR ELECTROMAGNETIC WAVES (2009) (17)
Iterative Methods for Solving the Exterior Dirichlet Problem for the Helmholtz Equation with Applications to the Inverse Scattering Problem for Low Frequency Acoustic Waves. (1980) (17)
Simultaneous Reconstruction of Shape and Impedance in Corrosion Detection (2010) (16)
On the convergence of successive approximations for an integral equation in a Green's function approach to the dirichlet problem (1976) (16)
A boundary integral equation method for a Neumann boundary problem for force-free fields (1981) (15)
A collocation method for a hypersingular boundary integral equation via trigonometric differentiation (2014) (15)
Simultaneous reconstruction of shape and generalized impedance functions in electrostatic imaging (2014) (15)
Karp’s theorem in electromagnetic scattering theory (1988) (15)
Conformal mapping and impedance tomography (2010) (15)
Conformal mapping and an inverse impedance boundary value problem (2006) (14)
Inverse problems and conformal mapping (2012) (14)
THE CONSTRUCTION OF SOLUTIONS TO ACOUSTIC SCATTERING PROBLEMS IN A SPHERICALLY STRATIFIED MEDIUM. II (1978) (14)
Reconstruction of extended sources for the Helmholtz equation (2013) (14)
The treatment of a Neumann boundary value problem for force-free fields by an integral equation method (1978) (14)
One-dimensional profile inversion of a cylindrical Layer with inhomogeneous impedance boundary: a Newton-type iterative solution (2005) (13)
On mixed boundary value problems for the Helmholtz equation (1977) (12)
A Factorization Method for an Inverse Neumann Problem for Harmonic Vector Fields (2003) (11)
Numerical methods in inverse obstacle scattering (2000) (10)
On Trefftz’ integral equation for the Bernoulli free boundary value problem (2017) (10)
ON A QUADRATURE METHOD FOR A LOGARITHMIC INTEGRAL EQUATION OF THE FIRST KIND (2008) (10)
Treatment of the Prager Problem of Potential Theory by the Integral Equation Method (1969) (10)
A conformal mapping method in inverse obstacle scattering (2014) (9)
A Sampling Method For An Inverse Boundary Value Problem For Harmonic Vector Fields (2002) (9)
On the existence of a solution to a singular integral equation in electromagnetic reflection (1980) (8)
An iterative method for a two-dimensional inverse scattering problem for a dielectric (2012) (8)
Nonlinear integral equations for Bernoulli's free boundary value problem in three dimensions (2017) (7)
Electrical impedance tomography using a point electrode inverse scheme for complete electrode data (2011) (7)
Singular Integral Equations (1999) (7)
Convergence of Discrete Green's Functions for Finite Difference Schemes (1985) (7)
On the Treatment of a Dirichlet–Neumann Mixed Boundary Value Problem for Harmonic Functions by an Integral Equation Method (1977) (7)
A nonlinear integral equation and an iterative algorithm for an inverse source problem (2015) (7)
A second degree Newton method for an inverse obstacle scattering problem (2011) (7)
L2‐boundary integral equations for the robin problem (1984) (6)
Chapter 1.4.1 – Specific Theoretical Tools (2002) (6)
Specific Theoretical Tools (2002) (5)
Electrical impedance tomography with point electrodes (2010) (5)
Chapter 1.4.2 – Scattering by Obstacles (2002) (5)
A boundary integral equation for the transmission eigenvalue problem for Maxwell equation (2018) (4)
Non-linear integral equations for the complete electrode model in inverse impedance tomography (2008) (4)
Fredholm's alternative for compact bilinear forms in reflexive Banach spaces (1977) (4)
A conformal mapping algorithm for the Bernoulli free boundary value problem (2016) (4)
Scattering by Obstacles (2002) (4)
Thirty years and still counting (2009) (4)
A singular perturbation problem for linear operators with an application to electrostatic and magnetostatic boundary and transmission problems (1981) (3)
On the Condition Number of Boundary Integral Equations in Acoustic Scattering using Combined Double- and Single-Layer Potentials (1985) (3)
Singular Boundary Integral Equations (2014) (3)
Inverse scattering for shape and impedance revisited (2018) (3)
Integral Equation Methods in Inverse Obstacle Scattering with a Generalized Impedance Boundary Condition (2018) (3)
Chapter 1: The Riesz–Fredholm Theory for Compact Operators (2013) (3)
A Global Analysis of Secondary Bifurcations in the Benard Problem and the Relationship between the Benard and Taylor Problems (1991) (3)
The Maxwell Equations (2019) (3)
Inverse Acoustic Obstacle Scattering (2013) (3)
On general Hermite trigonometric interpolation (1972) (2)
A Modified Integral Equation Method for the Electric Boundary-Value Problem for the Vector Helmholtz Equation (1980) (2)
Iterative methods for planar crack reconstruction in semi-infinite domains (2008) (2)
Three dimensional reconstructions in inverse obstacle scattering (1991) (2)
8. Some old and some new results in inverse obstacle scattering (2019) (2)
On the Low Wave Number Behavior of Two-Dimensional Scattering Problems for an Open Arc (1999) (2)
Nonlocal impedance conditions in direct and inverse obstacle scattering (2018) (2)
ON AN ILL–POSED PROBLEM FOR CONSTANT ALPHA FORCE-FREE FIELDS (1987) (2)
Inverse Scattering Theory (1989) (2)
Iterative Methods for Nonlinear Systems (1998) (2)
On boundary integral equation methods in stationary electromagnetic reflection (1981) (2)
The Inverse Medium Problem (2019) (2)
Acoustic Waves in an Inhomogeneous Medium (2019) (2)
INTEGRAL EQUATIONS AND INVERSE BOUNDARY VALUE PROBLEMS (2007) (1)
INTEGRAL EQUATIONS AND INVERSE BOUNDARY VALUE PROBLEMS (2007) (1)
INVERSE OBSTACLE SCATTERING WITH MODIFIED OR REDUCED DATA (2000) (1)
Ill-Conditioned Linear Systems (1998) (1)
The DB Boundary Condition in Electromagnetic Scattering Revisited (2021) (1)
Conformal mapping and impedance tomography (2010) (1)
On Error Norms of the Trapezoidal Rule (1978) (1)
Mathematical Methods of Plasmaphysics: Proceedings of a Conference held in Oberwolfach, September 16-22, 1979 (1980) (1)
DECOMPOSITION METHODS IN INVERSE OBSTACLE SCATTERING VIA NEWTON ITERATIONS (2004) (1)
On the Fredholm alternative (1983) (1)
Preface for Integral Equations and Inverse Boundry Value Problems (2007) (1)
Degenerate Kernel Approximation (2014) (0)
Buchbesprechungen - Book reviews - Notices bibliographiques: Low frequency scattering by G. Dassios, R. Kleinman (2002) (0)
Boundary Value Problems (1998) (0)
Book Reviews (2000) (0)
Bounded and Compact Operators (2014) (0)
Corrections to nonlinear integral equations for solving inverse boundary value problems for inclusions and cracks JIEA 18 (2006),13 38 (2010) (0)
Dual Systems and Fredholm Theory (1989) (0)
Corrigendum to "On the numerical solution of a hypersingular integral equation in scattering theory" [J. Comput. Appl. Math. 61(1995) 345-360] (2011) (0)
High-order methods for computational wave propagation and scattering organized (2014) (0)
Iterative Methods for Linear Systems (1998) (0)
Estimating errors of numerical approximation for periodic analytic functions (1977) (0)
Obstacle Scattering as Seen by R . K . and (2007) (0)
Chapter 2: Regularity Properties of Surface Potentials (2013) (0)
Surface impedance determination of an object located over a planar PEC surface and its use in shape reconstruction (2017) (0)
Free and Mixed Boundary Value Problems: Proceedings of a Conference held in Oberwolfach, April 16-22, 1978 (1995) (0)
The Heat Equation (2014) (0)
Regularization by Discretization (2014) (0)
Chapter 4: Boundary-Value Problems for the Time-Harmonic Maxwell Equations and the Vector Helmholtz Equation (2013) (0)
Initial Value Problems (1998) (0)
Regularization in Dual Systems (2014) (0)
TOPICAL REVIEW: Using fundamental solutions in inverse scattering (2006) (0)
Electromagnetic Waves in an Inhomogeneous Medium (2019) (0)
Chapter 9: Optimal Control Problems in Radiation and Scattering Theory (2013) (0)
Matrix Eigenvalue Problems (1998) (0)
Wave propagation: Mathematical Analysis and Simulation (2005) (0)
Introduction and Basic Functional Analysis (2014) (0)
The Riesz Theory (1989) (0)
The Vector Helmholtz Equation Revisited: Inverse Obstacle Scattering (2022) (0)
Chapter 3: Boundary-Value Problems for the Scalar Helmholtz Equation (2013) (0)
Chapter 7: Improperly Posed Problems and Compact Families (2013) (0)
Basic Functional Analysis (1998) (0)
On Trefftz’ integral equation for the Bernoulli free boundary value problem (2016) (0)
Iterative Solution and Stability (2014) (0)
An Inverse Boundary Value Problemfor the Heat Equation : the Neumann ConditionRoman Chapko (0)
Dual Systems and Fredholm Alternative (2014) (0)
Chapter 8: The Determination of the Shape of an Obstacle from Inexact Far-Field Data (2013) (0)
Obstacle Scattering as Seen by R.K. and R.K. (2019) (0)
Inverse Electromagnetic Obstacle Scattering (2019) (0)
Chapter 6: The Inverse Scattering Problem: Exact Data (2013) (0)
Direct Acoustic Obstacle Scattering (2013) (0)
The Helmholtz Equation (2019) (0)
Inverse Boundary Value Problems (2014) (0)
Chapter 5: Low Frequency Behavior of Solutions to Boundary-Value Problems in Scattering Theory (2013) (0)
Equations of the First Kind (2014) (0)

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What Schools Are Affiliated With Rainer Kress?

Rainer Kress is affiliated with the following schools:

University of Göttingen

Rainer Kress's Academic­Influence.com Rankings

Why Is Rainer Kress Influential?

Rainer Kress's Published Works

Published Works

What Schools Are Affiliated With Rainer Kress?

Rainer Kress's AcademicInfluence.com Rankings