This manuscript introduces the first hp-adaptive mesh refinement algorithm for the Theory of Functional Connections (TFC) to solve hypersensitive two-point boundary-value problems (TPBVPs). The TFC ...is a mathematical framework that analytically satisfies linear constraints using an approximation method called a constrained expression. The constrained expression utilized in this work is composed of two parts. The first part consists of Chebyshev orthogonal polynomials, which conform to the solution of differentiation variables. The second part is a summation of products between switching and projection functionals, which satisfy the boundary constraints. The mesh refinement algorithm relies on the truncation error of the constrained expressions to determine the ideal number of basis functions within a segment’s polynomials. Whether to increase the number of basis functions in a segment or divide it is determined by the decay rate of the truncation error. The results show that the proposed algorithm is capable of solving hypersensitive TPBVPs more accurately than MATLAB R2021b’s bvp4c routine and is much better than the standard TFC method that uses global constrained expressions. The proposed algorithm’s main flaw is its long runtime due to the numerical approximation of the Jacobians.
A novel time-domain algorithm is proposed in this paper for the iterative estimation of drive files. A drive file is a synchronized batch of dynamic time series commands that are simultaneously sent ...to one or more actuators in a test rig that is designed for service environment replication (SER). When drive file commands are input to an SER test rig, the response of the article under test is similar to what was measured in a service environment. The proposed Pulse Train Filtered-X Least Mean Square (PT-Fx-LMS) algorithm is based on methods developed for active noise and vibration control (ANVC). A time-domain PT-Fx-LMS algorithm is shown through several simulation studies to rapidly converge to a dynamic solution in a small number of iterations for a one degree-of-freedom nonlinear suspension. The PT-Fx-LMS algorithm is also shown to enable targeted iteration over isolated time slices within the data set, which challenges conventional frequency-domain techniques.
This paper proposes an energy-aware scheduling of malleable fork-join (MFJ) tasks on heterogeneous multicores. This work allows a task to be split into multiple sub-tasks for fork-join parallel ...execution. The number of the sub-tasks is determined simultaneously with scheduling. Our scheduling technique aims at the minimization of energy consumption under a deadline constraint. In addition, this paper proposes a technique for simultaneous scheduling and core-type optimization. The technique optimally decides types of cores (to be either "big" or "little") at the same time as MFJ task scheduling in order to further reduce energy consumption.
