Discretization of a boundary-value problem with the eXtended Element-Free Galerkin (X-EFG) method yields an asymmetric EFG-type Saddle-Point (EFG-SP) problem that is difficult to solve numerically. As high-performance solvers for the problem, four types of the Asymmetric-version improved Variable-Reduction Methods (AiVRMs) are formulated. A numerical code is developed for solving asymmetric EFG-SP problems with four types of AiVRMs and, by means of the code, performances of the four methods are investigated numerically.
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