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Conformal multi-symplectic integration methods for forced-damped semi-linear wave equations

机译:强迫阻尼半线性波动方程的保形多辛积分方法

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Conformal symplecticity is generalized to forced-damped multi-symplectic PDEs in 1 + 1 dimensions. Since a conformal multi-symplectic property has a concise form for these equations, numerical algorithms that preserve this property, from a modified equations point of view, are available. In effect, the modified equations for standard multi-symplectic methods and for space-time splitting methods satisfy a conformal multi-symplectic property, and the splitting schemes exactly preserve global symplecticity in a special case. It is also shown that the splitting schemes yield incorrect rates of energy/momentum dissipation, but this is not the case for standard multi-symplectic schemes. These methods work best for problems where the dissipation coefficients are small, and a forced-damped semi-linear wave equation is considered as an example.
机译:保形辛性一般化为1 + 1维的强制阻尼多辛PDE。由于保形多辛特性对于这些方程式具有简洁的形式,因此从修改的方程式角度来看,可以使用保留该特性的数值算法。实际上,用于标准多辛方法和时空拆分方法的修改方程满足保形多辛性质,并且拆分方案在特殊情况下精确地保留了全局辛。还显示了分裂方案产生不正确的能量/动量耗散率,但是对于标准的多辛方案则不是这种情况。这些方法最适合耗散系数小的问题,以强迫阻尼半线性波动方程为例。

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