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 ...

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 ...

Conformal mapping, a central concept in complex analysis, involves the transformation of one complex domain onto another while preserving local angles and shapes. This powerful tool has long been used ...

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 ...

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 ...

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 ...