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This letter presents the acceleration of locally one-dimensional finite-difference time-domain (LOD-FDTD) method using fundamental scheme on graphics processor units (GPUs). Compared to the conventional scheme, the fundamental LOD-FDTD (denoted as FLOD-FDTD) scheme has its right-hand sides cast in the simplest form without involving matrix operators. This leads to a substantial reduction in floating-point operations as well as field and coefficient memory access. To reap further advantages of FLOD-FDTD, certain field updates are embedded in the implicit solutions while exploiting the reuse of field data. Using FLOD-FDTD, it is found that significant speed-up is achievable for the method on GPUs.