Two-Dimensional Mesh Embedding for B-spline Methods
Two-Dimensional Mesh Embedding for B-spline Methods
复制标题
B 样条方法的二维网格嵌入
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
R. Moser
中科院分区：
文献类型：
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作者：
K. Shariff;R. Moser
许多因素促使人们考虑将B样条作为求解偏微分方程的基函数。这些都是任意数量级的精度和高分辨率类似的紧凑计划。此外，如果使用伽辽金方案，除了离散量的守恒之外，还可以获得能量等二次不变量的守恒。这项工作开发的另一个属性，即，能够处理半结构化的嵌入式或带状网格的二维几何形状。这可以大大减少许多应用中的网格点数量。提出了一种构造全局样条基的算法，该样条基在网格块边界处和其他地方一样自动具有d-1连续导数（遗传多项式次数）。基函数是一维B样条的简单适当的产品。整数和非整数细化比率都允许跨网格块。最后，线性标量方程，如泊松和平流方程的测试情况。
Many factors motivate consideration of B-splines as basis functions for solving partial differential equations. These are arbitrary orders of accuracy and high resolving powers similar to those of compact schemes. Furthermore, if one uses a Galerkin scheme one gets, in addition to conservation of the discretized quantities, conservation of quadratic invariants such as energy. This work develops another property, namely, the ability to treat semi-structured embedded or zonal meshes for two-dimensional geometries. This can drastically reduce the number of grid points in many applications. An algorithm is presented for constructing a global spline basis that automatically hasd-1 continuous derivatives at mesh-block boundaries as everywhere else (heredis the polynomial degree). The basis functions are simply suitable products of one-dimensional B-splines. Both integer and noninteger refinement ratios are allowed across mesh blocks. Finally, test cases for linear scalar equations such as the Poisson and advection equation are presented.