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Let $\Omega$ be an open, simply connected, and bounded region in $\mathbb{R}^{d}$, $d\geq2$, and assume its boundary $\partial\Omega$ is smooth. Consider solving an elliptic partial differential equation $Lu=f$ over $\Omega$ with zero Dirichlet bound
Externí odkaz:
http://arxiv.org/abs/1405.2567
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, and it is used in evaluating general polynomials over B_2 and B_3. The
Externí odkaz:
http://arxiv.org/abs/1307.5923
We present a spectral method for parabolic partial differential equations with zero Dirichlet boundary conditions. The region {\Omega} for the problem is assumed to be simply-connected and bounded, and its boundary is assumed to be a smooth surface.
Externí odkaz:
http://arxiv.org/abs/1203.6709
Autor:
Atkinson, Kendall, Hansen, Olaf
Consider being given a mapping \phi from the unit sphere S^{d-1}, d>2, to the smooth boundary of a simply-connected region \Omega in R^d. We consider the problem of constructing an extension \Phi from the unit ball B_d to \Omega. The mapping is requi
Externí odkaz:
http://arxiv.org/abs/1106.3338
Autor:
Atkinson, Kendall, Hansen, Olaf
Publikováno v:
Electronic Transactions on Numerical Analysis 37 (2010), pp. 386-412
Let $\Omega$ be an open, simply connected, and bounded region in $\mathbb{R}^{d}$, $d\geq2$, and assume its boundary $\partial\Omega$ is smooth. Consider solving the eigenvalue problem $Lu=\lambda u$ for an elliptic partial differential operator $L$
Externí odkaz:
http://arxiv.org/abs/0909.3607
Publikováno v:
Advances in Computational Mathematics 34 (2011), pp. 295-317
Let $\Omega$ be an open, simply connected, and bounded region in $\mathbb{R}^{d}$, $d\geq2$, and assume its boundary $\partial\Omega$ is smooth. Consider solving an elliptic partial differential equation $-\Delta u+\gamma u=f$ over $\Omega$ with a Ne
Externí odkaz:
http://arxiv.org/abs/0907.1270