A nonlocal dispersive optimal transport: Formulation and algorithm
We propose a unified framework that effectively characterizes challenging phenomena such as anomalous transport in heterogeneous media and long-range memory effects and interactions. This framework transports agent densities from a prescribed initial distribution to a terminal distribution while min...
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| Vydáno v: | Journal of computational and applied mathematics Ročník 476; s. 117132 |
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| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier B.V
01.04.2026
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| Témata: | |
| ISSN: | 0377-0427 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | We propose a unified framework that effectively characterizes challenging phenomena such as anomalous transport in heterogeneous media and long-range memory effects and interactions. This framework transports agent densities from a prescribed initial distribution to a terminal distribution while minimizing the associated energy cost. Motivated by optimal transport theory, we introduce a nonlocal dispersive optimal transport (NDOT) model governed by a space–time fractional partial differential equation (PDE). We solve the NDOT formulation using the general-proximal primal–dual hybrid gradient (G-prox PDHG) algorithm, and then introduce a novel preconditioner derived from the discretization of the space–time fractional PDE to accelerate the convergence. Numerical experiments – especially those with target states represented by power functions typical of fractional differential equation solutions – show that our model substantially reduces kinetic energy costs compared with its integer-order counterparts, highlighting its effectiveness and applicability for complex phenomena such as anomalous transport in heterogeneous environments. |
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| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2025.117132 |