傳統上高階內插近似的點集是以優化的方式求得。本文先介紹一幾何投影的方式來尋求三角形域中適合高階內插近似的點集。我們發現本法所求得的點集亦適合做為高階內插近似的節點, 且利用這些點集所構成的近似函數其近似效果並不遜於傳統的方式所建構的高階內插近似函數。並將此點集配合上高階譜方法應用於二維波方程上, 從建構點集到實際計算做一完整的敘述。

The nodal sets in simplex for high-order interpolation approximation
were constructed by some optimal methods in tradition. In this thesis
we introduce a new method using projection to construct nodal sets
in simplex, and a general framework of constructing multidimensional
pseudospectral schemes for simulation wave equation. The nodal sets
from projection for approximation are as good as the results obtained
by traditional methods. Stable numerical simulations of model wave
equations are also conducted. The results are agreed with the theoretical
analysis.

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