The mapping is a useful technique for improving the performance of WENO method. However, for the existed mapped WENO methods, two weaknesses still need to be overcome. First, too much computational cost is used, the computational cost of mapped WENO method is around 43 of the original WENO method. Second, on the nonuniform meshes, too much memory space is used. We can take the WENO-RM method on nonuniform rectangle meshes for example, which is one of the famous mapped WENO methods. Comparing to original WENO method, the WENO-RM needs to store 128×M additional parameters, where M is the cell number. In order to overcome these weaknesses, we propose a new strategy for implementing the mapped WENO method. Different from the previous works, the new strategy is based on the average weight. The new strategy has following major advantages: first, it can give the solution which is as accurate as the original mapped WENO method; second, it can save the computational cost, because it only uses slightly more computational cost than the original WENO method; third, it can save the memory space because it only needs to store a little additional parameter compared to the original WENO method.

中文翻译：

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一种实现映射WENO方法的新策略

映射是提高 WENO 方法性能的有用技术。然而，对于现有的映射 WENO 方法，仍有两个弱点需要克服。首先，使用了太多的计算成本，mapped WENO 方法的计算成本在43原WENO方法。其次，在非均匀网格上，使用了过多的内存空间。我们可以以非均匀矩形网格上的 WENO-RM 方法为例，这是著名的映射 WENO 方法之一。与原来的 WENO 方法相比，WENO-RM 需要存储128×米附加参数，其中米是单元格编号。为了克服这些弱点，我们提出了一种实现映射 WENO 方法的新策略。与以往作品不同的是，新策略是基于平均权重。新策略具有以下主要优点：首先，它可以给出与原始映射WENO方法一样准确的解决方案；其次，它可以节省计算成本，因为它只比原来的WENO方法使用了稍微多一点的计算成本；第三，它可以节省内存空间，因为与原来的WENO方法相比，它只需要存储一点额外的参数。