Spectrally accurate solutions to inhomogeneous elliptic PDE in smooth geometries using function intension

We present a spectrally accurate embedded boundary method for solving linear, inhomogeneous, elliptic partial differential equations (PDE) in general smooth geometries two dimensions, focusing this manuscript on the Poisson, modified Helmholtz, and Stokes equations. Unlike several recently proposed methods which rely function extension, we propose instead utilizes intension, or truncation of known values. Similar to those based once inhomogeneity is truncated may solve PDE using any many simple, fast, robust solvers that have been developed regular grids simple domains. Function intension inherently stable, as are all steps solution method, can be used domains do not readily admit extensions. pay price exchange improved stability flexibility: addition domain, must additionally (1) small auxiliary domain fitted boundary, (2) ensure consistency across interface between rest physical domain. show how these tasks accomplished efficiently (in both asymptotic practical sense), compare convergence recent high-order schemes. Finally, demonstrate wide applicability nonlinear predator-prey model, achieving rapid space time.