论文标题
使用扩展的DG方法，在多维无界域上有效的双曲线 - 羟基蛋白模型
Efficient hyperbolic-parabolic models on multi-dimensional unbounded domains using an extended DG approach
论文作者
论文摘要
我们引入了多维半无限域的双曲线 - 羟基蛋白酶问题的扩展不连续的Galerkin离散化。在先前的一维情况下，我们将带状的计算域分为有限的区域，通过使用Legendre基函数的不连续有限元素和无限的子域进行离散的区域，其中将缩放的laguerre函数用作基础。界面处的数值通量允许两个区域的无缝耦合。结果表明，所得的耦合策略可在线性和非线性标量和矢量模型问题的测试中产生准确的数值解决方案。另外，可以在域的半无限部分中模拟有效的吸收层，以湿润界面处的带有伪造反射可忽略不计的信号。通过调整Laguerre基础函数的缩放参数，扩展的DG方案模拟了大型空间尺度上的瞬态动力学，与标准的单域不连续的有限元技术相比，在给定精度水平上的计算成本大大降低。
We introduce an extended discontinuous Galerkin discretization of hyperbolic-parabolic problems on multidimensional semi-infinite domains. Building on previous work on the one-dimensional case, we split the strip-shaped computational domain into a bounded region, discretized by means of discontinuous finite elements using Legendre basis functions, and an unbounded subdomain, where scaled Laguerre functions are used as a basis. Numerical fluxes at the interface allow for a seamless coupling of the two regions. The resulting coupling strategy is shown to produce accurate numerical solutions in tests on both linear and non-linear scalar and vectorial model problems. In addition, an efficient absorbing layer can be simulated in the semi-infinite part of the domain in order to damp outgoing signals with negligible spurious reflections at the interface. By tuning the scaling parameter of the Laguerre basis functions, the extended DG scheme simulates transient dynamics over large spatial scales with a substantial reduction in computational cost at a given accuracy level compared to standard single-domain discontinuous finite element techniques.
