Abstract
Finite difference techniques have played a dominant role in numerical relativity. This situation will likely prevail; for instance, the current grand challenge effort in the United States to simulate, by the end of the century, black-hole collisions is entirely based on finite difference codes. Furthermore, the power of finite difference techniques has recently been enhanced with the implementation of adaptive mesh refinements. In spite of the finite difference success, there have been a significant number of numerical studies in gravitation in which finite difference methods are either not used, or applied in combination with other techniques. These lectures review four alternative approaches to numerical relativity from those of finite difference. The first lecture addresses solutions to the initial-data problem in general relativity using multiquadrics and finite elements methods. The second lecture reviews particle-mesh and smoothed particle hydrodynamics methods used in conjunction with finite differences to solve the Einstein-hydro field equations.
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