Spectral domain embedding for elliptic PDEs in complex domains

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The hp‐d‐adaptive finite cell method for geometrically nonlinear problems of solid mechanics (2012, methodology): “The fictitious domain approach has been widely used in conjunction with penalty methods [9–11], the mortar approach [12], Lagrange multipliers [8,13–15], Nitsche’s method [16], extended FE [17–20], discontinuous Galerkin [21], and spectral methods [22,23] to address problems of structural analysis, ”
Fourier spectral methods for fractional-in-space reaction-diffusion equations (2014, background): “However, recent work in combining spectral methods with domain embedding techniques has allowed the extension of these methods to irregular domains [27, 35, 36, 37, 38].”