An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
Improved-accuracy algorithms for time-domain finite methods in electromagnetics
Improved-accuracy algorithms for time-domain finite methods in electromagnetics
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The finite element time domain (FETD) method is commonly used for transient simulation of electromagnetic wave phenomena. Most practitioners consider FETD, when time integrated using the Newmark-Beta method, to be unconditionally stable when @b=0.25. Unlike the finite difference time domain (FDTD) ''courant criterion'', FETD-Newmark has no limiting timestep above which the method exhibits exponential growth. However, herein the stability properties of FETD-Newmark will be rigorously investigated by deducing the Jordan canonical form of the FETD-Newmark amplification matrix, and it will be demonstrated that the method does exhibit linear growth for certain field configurations. These modes are none other than the pure-gradient fields associated with ''late time instability''. Though many practical simulations are of short duration and will never observe a linearly growing gradient solution, it can be problematic for simulations which require long time periods to be integrated. A correction scheme for eliminating this late time instability shall be suggested, and numerical results will verify its performance.