Integral Equation Methods

Shidong Jiang, Mary Catherine A. Kropinski, and Bryan Quaife (2013), Second Kind Integral Equation Formulation for the Modified Biharmonic Equation and its Applications, accepted J. Comp. Phys., 29 pages

Mary Catherine A. Kropinski and Bryan Quaife (2011), Fast Integral Equation Methods Applied for Rothe's Method Applied to the Isotropic Heat Equation, accepted Comp. Math. Appl., 22 pages.

Mary Catherine Kropinski and Enkeleida Lushi (2011), Efficient Numerical Methods for Multiple Surfactant-Coated Bubbles in a Two-Dimensional Stokes Flow, accepted J. Comp. Phys., 34 pages.

Mary Catherine A. Kropinski and Bryan Quaife (2011), Fast Integral Equation Methods for the Modified Helmholtz Equation, J. Comp. Phys. 230, 425-434.

Leslie Greengard and Mary Catherine Kropinski (2004), Integral Equation Methods for Stokes Flow in Doubly-Periodic Domains, J.Eng.Math. 48, 157-170.

M.C.A. Kropinski (2002), Numerical Methods for Multiple Interfaces in Creeping Flows, J.Comp.Phys. 180, 1-24.

Mary Catherine A. Kropinski, Time-Evolving Interfaces in a Stokes Flow, Scientific Computing and Applications, Adv. Comput. Theory Pract. 7, 83-90.

M.C.A. Kropinski (2001), An Efficient Numerical Method for Studying Interfacial Motion in Two-Dimensional Creeping Flows, J. Comp. Phys. 171, 479-508.

M.C.A. Kropinski (1999), Integral Equation Methods for Particle Simulations in Creeping Flows , Comp. Math. Appl. v. 38, 67-87.

L. Greengard and M.C.A. Kropinski (1998), An Integral Equation Approach to the Incompressible Navier-Stokes Equations in Two Dimensions , SIAM J. Sci. Comput. 20, 318-336.

Leslie Greengard, Mary Catherine Kropinski and Anita Mayo (1996), Integral equation methods for Stokes flow and isotropic elasticity in the plane , J. Comp. Phys. 125, 403-414.

Hybrid Aysmptotic-Numerical Techniques

M.C. Kropinski, A.E. Lindsay, and M.J. Ward (2010), Asymptotic Analysis of Localized Solutions to Some Linear and Nonlinear Biharmonic Eigenvalue Problems, accepted to Studies in Appl. Math., 43 pages.

M. Titcombe, M.C.A. Kropinski and M.J. Ward (2000), A Hybrid Asymptotic-Numerical Solution for Low Reynolds Number Flow Past an Asymmetric Cylindrical Body, Studies in Appl. Math. 105, 165-190.

M.C.A. Kropinski, Michael J. Ward, and Joseph B. Keller (1995), A hybrid asymptotic-numerical scheme for calculating low Reynolds number flow past cylindrical profiles , SIAM J. Appl. Math. 55 No. 6., 1484-1510.


M.C.A. Kropinski (2007), Creeping Flow, McGraw-Hill Encyclopedia of Science and Technology.

P.A. Forsyth and M.C.A. Kropinski (1997), Monotonicity Considerations for Saturated-Unsaturated Subsurface Flow, SIAM J. Sci. Comput. 18, 1328-1354.

M.C.A. Kropinski (1997), On the Design of Lifting Airfoils with High Critical Mach Number Using Full Potential Theory , Theoret. Comput. Fluid Dynamics 9, 17-32.

M.C.A. Kropinski, D.W. Schwendeman, and J.D. Cole (1995), Hodograph design of lifting airfoils with high critical Mach numbers , Theoret. Comput. Fluid Dynamics 7, 173-188.

D.W. Schwendeman, M.C.A. Kropinski, and J.D. Cole (1993), On the construction and calculation of optimal nonlifting critical airfoils , ZAMP 44, 556-571.

J.D. Cole, M.C. Kropinski, D.W.Schwendeman (1991), A Study of Critical Airfoils, Proc. 4th Int. Symp.Comp.Fluid Dyn., 664-669.