Engineers have designed a metamaterial device that can solve integral equations. The device works by encoding parameters into the properties of an incoming electromagnetic wave; once inside, the ...

Electromagnetic integral equations offer a powerful framework for modelling wave propagation and scattering phenomena by recasting Maxwell’s equations into formulations involving integrals over ...

We consider solving integral equations on a piecewise smooth surface S in R3 with a smooth kernel function, using piecewise polynomial collocation interpolation of the surface. The theoretical ...

Analogue computer: Brian Edwards (left), Nader Engheta (centre) and Nasim Mohammadi Estakhri show-off their microwave protoype. (Courtesy: Eric Sucar/University of Pennsylvania) Metamaterials have ...

SIAM Journal on Applied Mathematics, Vol. 75, No. 3 (2015), pp. 929-952 (24 pages) We present a new class of well-conditioned integral equations for the solution of two and three dimensional ...

Integral equations in various scientific theories and their relation to differential equations. Methods of solving linear problems with Hilbert Schmidt, Cauchy, and Wiener-Hopf type kernels; ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...