The target of this research is to resolve high-dimensional partial differential equations (PDEs) for multi-asset options, modeled as parabolic time-dependent PDEs. We present a hybrid radial basis function - finite difference (RBF-FD) solver, which combines the advantages of Gaussian and multiquadric functions. Additionally, we employ the Krylov subspace method on the resulting system of ordinary differential equations, reducing the computation load for finding the numerical solution. Computational tests, up to seven dimensions, and comparisons support the superiority of our hybrid solver. 

Numerical investigation of high-dimensional option pricing PDEs by utilizing a hybrid radial basis function - finite difference procedure

This Innovations Deserving Exploratory Analysis (IDEA) project developed and evaluated a prototype system, from bench-scale tests to actual field trials, to continuously measure and control, on line and in real-time every 5 minutes, aggregate gradation in hot-mix asphalt plants. By applying this novel technology, asphalt plants are expected to (a) deliver an asphalt product that complies with the job mix formula, (b) run more uniformly with fewer dead periods, (c) require less asphalt and aggregates for the same throughput, and (d) produce better pavement with a higher performance-to-cost ratio. This IDEA project was structured in two phases. Phase 1 consisted of determining the feasibility of the concept in a laboratory prototype setup and a pilot-scale arrangement. During Phase 2, the implementation and testing of a full-scale prototype was conducted at Staker Company in Salt Lake City, Utah.

On line real-time measurement and control of aggregate gradation in asphalt plants

Modified space-time radial basis function collocation method for solving three-dimensional transient elastodynamic problems

Optimizing shape parameters in RBF methods: A systematic review of techniques, applications, and computational challenges

Red mud is a solid residue that results when bauxite ore is processed to obtain alumina (aluminum oxide –Al 2 O 3 ), the main chemical compound to produce aluminum. Brazil has a wide reserve of bauxite in Para State and the ore is processed in large scale. However, in the country red mud is stored inadequately in the environment. Para is situated in northern region of Brazil and presents high temperature throughout the year. The elevated traffic volume and the high temperatures contributed to the early appearing of defects in the flexible asphalt pavement surfaces. This laboratory study aims the introduction of the red mud as filler in dense asphalt mixtures to improve the permanent deformation resistance. Asphalt mixtures with 3%, 5% and 7% of red mud (range between 0.02 to 2,800 micrometers) were produced. A conventional mixture with 7% stone powder filler (maximum diameter of 0.075 mm) was used as reference. Permanent deformation resistance of the mixtures was evaluated through French Rutting Tester. As a result, the mixture with 5% red mud presented better resistance that obtained at 30,000 cycles, 3.5% of rutting percentage depth. The asphalt mixtures with red mud presented good performance, with reduction of the permanent deformation of 12.63 to 42.62% in relation to reference mixture. Red mud as filler in asphalt mixtures is a viable option to reuse this waste, as well as being an environmentally friendly alternative.

/pdf/mechanical-feasibility-of-using-red-mud-as-filler-in-asphalt-c8kmsq3c6u.pdf

Mechanical feasibility of using red mud as filler in asphalt mixtures to improve permanent deformation

Iterative optimization method for determining optimal shape parameter in RBF-FD method

Digital Mix Design for Performance Optimization of Asphalt Mixture

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Iterative optimization method for determining optimal shape parameter in RBF-FD method

Digital Mix Design for Performance Optimization of Asphalt Mixture