K. Atkinson

activity

20082014

most citedA Spectral Method for Elliptic Equations: The Neumann Problem

32 citations · 82 across the 7 of their papers we have counts for

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7 papers · 1 filter

math.NA2014

A Spectral Method for Nonlinear Elliptic Equations

Kendall Atkinson, David Chien, Olaf Hansen

Let $Ω$ be an open, simply connected, and bounded region in $R^{d}$ , $d \geq 2$ , and assume its boundary $\partial Ω$ is smooth. Consider solving an elliptic partial differen…

math.NA2013

Evaluating Polynomials Over the Unit Disk and the Unit Ball

Kendall Atkinson, Olaf Hansen, David Chien

We investigate the use of orthonormal polynomials over the unit disk B_2 in R^2 and the unit ball B_3 in R^3. An efficient evaluation of an orthonormal polynomial basis is given, a…

math.NA2012

A Spectral Method for Parabolic Differential Equations

Kendall Atkinson, Olaf Hansen, David Chien

We present a spectral method for parabolic partial differential equations with zero Dirichlet boundary conditions. The region Ω for the problem is assumed to be simply-connected an…

math.NA2011★ 11 cited

Creating domain mappings

Kendall Atkinson, Olaf Hansen

Consider being given a mapping ϕfrom the unit sphere S^{d-1}, d>2, to the smooth boundary of a simply-connected region Ωin R^d. We consider the problem of constructing an extension…

math.NA2009★ 11 cited

A Spectral Method for the Eigenvalue Problem for Elliptic Equations

Kendall Atkinson, Olaf Hansen

Let $Ω$ be an open, simply connected, and bounded region in $R^{d}$ , $d \geq 2$ , and assume its boundary $\partial Ω$ is smooth. Consider solving the eigenvalue problem $Lu=λ…

math.NA2009★ 32 cited

A Spectral Method for Elliptic Equations: The Neumann Problem

Kendall Atkinson, David Chien, Olaf Hansen

Let $Ω$ be an open, simply connected, and bounded region in $R^{d}$ , $d \geq 2$ , and assume its boundary $\partial Ω$ is smooth. Consider solving an elliptic partial differen…