计算机代数遇上有限元：麦克斯韦方程组的高效实现
Computer Algebra meets Finite Elements: an Efficient Implementation for Maxwell's Equations
AI总结：
针对时域麦克斯韦方程组，采用能量守恒间断伽辽金有限元格式，利用形状函数的递推性质和张量积结构实现高阶近似的高效计算，其中递推关系通过计算机代数方法（如完整系统方法）符号推导得到。
摘要：
我们考虑使用能量守恒的间断伽辽金有限元格式对时域麦克斯韦方程组进行数值离散。该特定格式允许对电场和磁场进行高阶近似。我们特别强调高效实现，通过利用所选形状函数的递推性质和张量积结构来实现。这些递推关系已通过计算机代数方法（类似于完整系统方法）符号推导得到。
英文摘要：
We consider the numerical discretization of the time-domain Maxwell's equations with an energy-conserving discontinuous Galerkin finite element formulation. This particular formulation allows for higher order approximations of the electric and magnetic field. Special emphasis is placed on an efficient implementation which is achieved by taking advantage of recurrence properties and the tensor-product structure of the chosen shape functions. These recurrences have been derived symbolically with computer algebra methods reminiscent of the holonomic systems approach.
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