Abstract
The time-dependent Ginzburg-Landau equations describing a $d$-wave superconductor are simulated by the finite-element method. The equilibrium vortex structure in bulk samples, the nature of vortices in bulk and finite-size samples subject to various types of pinnings, and the transport behaviors are addressed. The extended finite-element method proves to be flexible to deal with various types of boundary conditions, desirable to simulate relaxation processes with very long time scales as well as the dynamics of vortices, especially in high-$\ensuremath{\kappa}$ superconductors.
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