Good neighborhoods for multidimensional Van Leer limiting
Journal of Computational Physics
Incremental remapping as a transport&slash;advection algorithm
Journal of Computational Physics
Second-order sign-preserving conservative interpolation (remapping) on general grids
Journal of Computational Physics
An efficient linearity-and-bound-preserving remapping method
Journal of Computational Physics
An Optimization-Based Approach for the Design of PDE Solution Algorithms
SIAM Journal on Numerical Analysis
Additive operator decomposition and optimization–based reconnection with applications
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Optimization-Based modeling with applications to transport: part 2. the optimization algorithm
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Optimization-Based modeling with applications to transport: part 3. computational studies
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Optimization-Based modeling with applications to transport: part 2. the optimization algorithm
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Optimization-Based modeling with applications to transport: part 3. computational studies
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Journal of Computational Physics
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This paper is the first of three related articles, which develop and demonstrate a new, optimization---based framework for computational modeling. The framework uses optimization and control ideas to assemble and decompose multiphysics operators and to preserve their fundamental physical properties in the discretization process. An optimization---based monotone, linearity preserving algorithm for transport (OBT) demonstrates the scope of the framework. The second and the third parts of this work focus on the formulation of efficient optimization algorithms for the solution of the OBT problem, and computational studies of its accuracy and efficacy.