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Hammer head sand casting optimization shows the product (lower region) and riser and gating system (upper region) during the solidification of the initial design (left) and optimized design (right). Yellow indicates the molten metal. Note how a molten region is isolated in the hammer head in the initial design near the end of the solidification. This leads to undesirable porosity in the product. The porosity is eliminated in the optimized design by optimizing the geometry of the gating system to minimize its mass subject to directional solidification constraints. Byrne, P. E., D. A. Tortorelli, and J. A. Dantzig, "Solidification Control by Numerical Optimization," Visualization of Engineering Research, 1:1, 1995