Frank Rizzo and boundary integral equations

Abstract Frank Rizzo was a pioneer in what he called boundary integral equation methods. With his students and colleagues, he developed theory and algorithms for many problems of engineering interest. In this memorial paper, we review his life and work. A list of his publications is included.

[1]  Frank J. Rizzo,et al.  A boundary integral approach to potential and elasticity problems for axisymmetric bodies with arbitrary boundary conditions , 1979 .

[2]  Frank J. Rizzo,et al.  On hypersingular boundary integral equations for certain problems in mechanics , 1989 .

[3]  Time-Harmonic Elastic-Wave Scattering: The Role of Hypersingular Boundary Integral Equations , 1991 .

[4]  B. C. Smiley,et al.  Optic nerve axoplasm and papilledema. , 1975, Survey of ophthalmology.

[5]  Yijun Liu,et al.  Regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions , 1995 .

[6]  Scattering of Acoustic and Elastic Waves by Cracklike Objects: The Role of Hypersingular Integrals , 1992 .

[7]  Frank J. Rizzo,et al.  An integral equation approach to boundary value problems of classical elastostatics , 1967 .

[8]  F. Rizzo,et al.  Intraocular axonal swelling produced by partial, immediately retrobulbar ligature of optic nerve. , 1977, Investigative ophthalmology & visual science.

[9]  F. J. Rizzo,et al.  A unified boundary integral equation method for a class of second order elliptic boundary value problems , 1984, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[10]  Ibrahim Elshafiey,et al.  General formulation for light scattering by a dielectric body near a perfectly conducting surface , 1996 .

[11]  T. Cruse,et al.  A direct formulation and numerical solution of the general transient elastodynamic problem. II , 1968 .

[12]  On the computation of two-dimensional stress intensity factors using the boundary element method , 1988 .

[13]  Early Development of the BEM at the University of Kentucky , 2007 .

[14]  A. Seybert,et al.  An advanced computational method for radiation and scattering of acoustic waves in three dimensions , 1985 .

[15]  F. J. Rizzo,et al.  A weakly singular form of the hypersingular boundary integral equation applied to 3-D acoustic wave problems , 1992 .

[16]  F. J. Rizzo,et al.  The direct boundary integral equation method for the three-dimensional elastodynamic transmission problem , 1991 .

[17]  Yijun Liu,et al.  Boundary integral equations for thin bodies , 1994 .

[18]  T. A. Cruse.  Boundary Integral Equations - A Personal View , 2001 .

[19]  Frank J. Rizzo,et al.  Direct boundary integral equations for elastodynamics in 3-D half-spaces , 1990 .

[20]  F. J. Rizzo,et al.  A formulation and solution procedure for the general non-homogeneous elastic inclusion problem , 1968 .

[21]  Frank J. Rizzo,et al.  Three‐dimensional crack analysis using singular boundary elements , 1989 .

[22]  F. Rizzo,et al.  PARTITIONING, BOUNDARY INTEGRAL EQUATIONS, AND EXACT GREEN'S FUNCTIONS , 1995 .

[23]  L. Schmerr,et al.  Hypersingular Integral Equations for Crack Problems , 1989 .

[24]  Frank J. Rizzo.  The Boundary Element Method Some Early History — A Personal View , 1989 .

[25]  Frank J. Rizzo,et al.  On boundary integral equations for crack problems , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[26]  F. Rizzo,et al.  Overcoming Nonuniqueness in the Direct BIEM for Three-Dimensional Steady-State Exterior Elastodynamic Problems , 1990 .

[27]  L. Schmerr,et al.  Discretization Considerations with Hypersingular Integral Formulas for Crack Problems , 1990 .

[28]  R. B. Thompson,et al.  Boundary element method solutions for elastic wave scattering in 3D , 1993 .

[29]  Frank J. Rizzo,et al.  Elastic scatterer interaction via generalized Born series and far-field approximations , 1993 .

[30]  Thomas J. Rudolphi,et al.  Acoustic Scattering by Submerged Elastic Bodies: A Boundary Element Approach , 1990 .

[31]  Frank J. Rizzo,et al.  An advanced boundary integral equation method for three‐dimensional thermoelasticity , 1977 .

[32]  Yijun Liu,et al.  Scattering of elastic waves from thin shapes in three dimensions using the composite boundary integral equation formulation , 1997 .

[33]  F. Rizzo,et al.  HYPERSINGULAR INTEGRALS: HOW SMOOTH MUST THE DENSITY BE? , 1996 .

[34]  F. Rizzo,et al.  Some efficient boundary integral strategies for time-harmonic wave problems in an elastic halfspace , 1998 .

[35]  Yijun Liu,et al.  Hypersingular boundary integral equations for radiation and scattering of elastic waves in three dimensions , 1993 .

[36]  Yijun Liu,et al.  Some advances in boundary integral methods for wave-scattering from cracks , 1992 .

[37]  F. J. Rizzo,et al.  A boundary element model for acoustic-elastic interaction with applications in ultrasonic NDE , 1990 .

[38]  F. J. Rizzo,et al.  Application of Overhauser C1 Continuous Boundary Elements to “Hypersingular” BIE for 3-D Acoustic Wave Problems , 1991 .

[39]  Frank J. Rizzo,et al.  On time-harmonic elastic-wave analysis by the boundary element method for moderate to high frequencies , 1986 .

[40]  Frank J. Rizzo,et al.  Boundary-element analysis of wave scattering from cracks , 1990 .

[41]  J. O. Watson,et al.  Boundary Elements from 1960 to the Present Day , 2007 .

[42]  Some observations on Kelvin's solution in classical elastostatics as a double tensor field with implications for Somigliana's integral , 1983 .

[43]  Thomas J. Rudolphi,et al.  Stress intensity sensitivities via Hypersingular boundary integral equations , 1999 .

[44]  F. J. Rizzo,et al.  An Application of the Correspondence Principle of Linear Viscoelasticity Theory , 1971 .

[45]  Frank J. Rizzo,et al.  Boundary-integral equation method : computational applications in applied mechanics : presented at 1975 Applied Mechanics Conference, the Rensselaer Polytechnic Institute, Troy, New York, June 23-25, 1975 , 1975 .

[46]  Frank J. Rizzo,et al.  A Method for Stress Determination in Plane Anisotropic Elastic Bodies , 1970 .

[47]  Lester W. Schmerr,et al.  Hypersingular Integral Formulas and Wave Scattering with the Boundary Element Method , 1988 .

[48]  Elastic Wave Scattering by Arbitrarily Shaped Voids , 1989 .

[49]  Hypersingular Boundary Integral Equations: A New Approach to Their Numerical Treatment , 1991 .

[50]  Frank J. Rizzo,et al.  A boundary integral equation method for radiation and scattering of elastic waves in three dimensions , 1985 .

[51]  F. Rizzo,et al.  An integral equation formulation of three dimensional anisotropic elastostatic boundary value problems , 1973 .

[52]  F. J. Rizzo,et al.  Nearly Singular and Hypersingular Integrals in the Boundary Element Method , 1970 .

[53]  F. Rizzo,et al.  Boundary element analysis for composite materials and a library of Green's functions , 1998 .

[54]  Graeme Fairweather,et al.  On the numerical solution of two-dimensional potential problems by an improved boundary integral equation method☆ , 1979 .

[55]  D. Clements.  Boundary value problems governed by second order elliptic systems , 1978 .

[56]  Norio Nakagawa,et al.  Progress in Eddy Current Modeling via the Boundary Element Method , 1997 .

[57]  F. Rizzo,et al.  A note on the body force integral of classical elastostatics , 1977 .

[58]  F. J. Rizzo,et al.  Continuity requirements for density functions in the boundary integral equation method , 1992 .

[59]  L. Schmerr,et al.  Hypersingular Boundary Integral Equations: Some Applications in Acoustic and Elastic Wave Scattering , 1990 .

[60]  F. J. Rizzo,et al.  A special integral equation formulation for acoustic radiation and scattering for axisymmetric bodies and boundary conditions , 1986 .

[61]  M. A. Jaswon.  Integral equation methods in potential theory. I , 1963, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[62]  F. J. Rizzo,et al.  Application of the boundary element method to elastic wave scattering by irregular defects , 1990 .

[63]  F. J. Rizzo,et al.  Application of the BIE Method to Sound Radiation Problems Using an Isoparametric Element , 1984 .

[64]  T. A. Cruse,et al.  Smoothness–relaxation strategies for singular and hypersingular integral equations , 1998 .

[65]  J. Watson,et al.  Effective numerical treatment of boundary integral equations: A formulation for three‐dimensional elastostatics , 1976 .

[66]  F. Rizzo,et al.  A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations , 1992 .

[67]  Frank J. Rizzo,et al.  A method of solution for certain problems of transient heat conduction , 1970 .

[68]  Yijun Liu,et al.  Eddy Current Analysis for 3-D Problems Using the Boundary Element Method , 1993 .

[69]  F. Rizzo,et al.  The boundary integral equation method with application to certain stress concentration problems in elasticity , 1981, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[70]  F. Rizzo.  The Finite and Boundary Element Methods: One View of Their Foundations , 1988 .

[71]  J. Wagner,et al.  AN ADVANCED BOUNDARY INTEGRAL EQUATION METHOD FOR TWO-DIMENSIONAL ELECTROMAGNETIC FIELD PROBLEMS* , 1977 .

[72]  F. Rizzo.  Springs, Formulas and Flatland:A Path to Boundary Integral Methods in Elasticity , 2007 .

[73]  P. A. Martin.  Maurice Jaswon and boundary element methods , 2012 .

[74]  F. Rizzo,et al.  A boundary element strategy for elastostatic inverse problems involving uncertain boundary conditions , 1999 .