Numerical analysis and the scientific method
IBM Journal of Research and Development - Mathematics and computing
Second-order accurate volume-of-fluid algorithms for tracking material interfaces
Journal of Computational Physics
A simple package for front tracking
Journal of Computational Physics
A Conservative Front Tracking Method in N-Dimensions
Journal of Scientific Computing
A coupling interface method for elliptic interface problems
Journal of Computational Physics
Journal of Computational Physics
Augmented coupling interface method for solving eigenvalue problems with sign-changed coefficients
Journal of Computational Physics
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Decompositions of the plane into disjoint components separated by curves occur frequently. We describe a package of subroutines which provides facilities for defining, building, and modifying such decompositions and for efficiently solving various point and area location problems. Beyond the point that the specification of this package may be useful to others, we reach the broader conclusion that well-designed data structures and support routines allow the use of more conceptual or non-numerical portions of mathematics in the computational process, thereby extending greatly the potential scope of the use of computers in scientific problem solving. Ideas from conceptual mathematics, symbolic computation, and computer science can be utilized within the framework of scientific computing and have an important role to play in that area.