A stable, efficient scheme for š^n function extensions on smooth domains in ā^d
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A new scheme is proposed to construct a š^n function extension for smooth functions defined on a smooth domain Dāā^d. Unlike the PUX scheme, which requires the extrapolation of the volume grid via an expensive ill-conditioned least squares fitting, the scheme relies on an explicit formula consisting of a linear combination of function values in D, which only extends the function along the normal direction. To be more precise, the š^n extension requires only n+1 function values along the normal directions in the original domain and ensures š^n smoothness by construction. When combined with a shrinking function and a smooth window function, the scheme can be made stable and robust for a broad class of domains with complex smooth boundary.
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