...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Journal of Computational Physics >Solving nonlinear parabolic PDEs in several dimensions: Parallelized ESERK codes
【24h】

Solving nonlinear parabolic PDEs in several dimensions: Parallelized ESERK codes

机译：求解非线性抛物面PDE在几个尺寸下：并联ESERK代码

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

There is a very large number of very important situations which can be modeled with nonlinear parabolic partial differential equations (PDEs) in several dimensions. In general, these PDEs can be solved by discretizing in the spatial variables and transforming them into huge systems of ordinary differential equations (ODEs), which are very stiff. Therefore, standard explicit methods require a large number of iterations to solve stiff problems. But implicit schemes are computationally very expensive when solving huge systems of nonlinear ODEs. Several families of Extrapolated Stabilized Explicit Runge-Kutta schemes (ESERK) with different order of accuracy (3 to 6) are derived and analyzed in this work. They are explicit methods, with stability regions extended, along the negative real semiaxis, quadratically with respect to the number of stages s, hence they can be considered to solve stiff problems much faster than traditional explicit schemes. Additionally, they allow the adaptation of the step length easily with a very small cost.
机译：有很多非常重要的情况可以用多维非线性抛物偏微分方程（PDE）来建模。一般来说，这些偏微分方程可以通过对空间变量进行离散并将其转化为非常僵硬的大型常微分方程组（ODE）来求解。因此，标准的显式方法需要大量迭代来解决刚性问题。但隐式格式在求解大型非线性常微分方程组时计算量非常大。本文推导并分析了几种不同精度（3到6）的外推稳定显式龙格-库塔格式（ESERK）。它们是显式方法，其稳定区域沿着负实半轴扩展，与阶段数s成二次关系，因此它们可以被认为比传统显式格式更快地解决刚性问题。此外，它们允许以非常小的成本轻松调整步长。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号