Rainer Kress
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Rainer Kressmathematics Degrees
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(Suggest an Edit or Addition)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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