CT1: Topics in numerical mathematics


Session A: Oct.1, 10:40am-12:00pm, Classroom Building 122
Session B: Oct.1, 3:10pm-4:30pm, Classroom Building 122

10:40am-11:00am (Oct 1)
CLB 122

Md Afsar Ali,
Kansas Wesleyan University

An age-and Phase-Structured Model of Malaria Parasite Replication in Erythrocytes and Anti-malarial Therapies.


Replication of Plasmodium parasites within human erythrocytes initiates malaria symptoms in blood. The cell division cycle of these parasites, however, is still poorly understood. In other eukaryotes, different cell-cycle synchronization techniques have been used to shed light on the mechanisms underlying cell division and control. In plasmodium, there is currently no method for cell-cycle synchronization. We investigate whether DNA synthesis inhibitors, mitotic spindle inhibitors, or cell-cycle control elements (such as cyclin-dependent kinases) can be used to synchronize P. falciparum cultures to a particular cell-cycle phase. For this, we develop an age-and-phase structured cell population balance model of cells differentiated by their position within the cell division cycle. A system of partial differential equations governs the kinetics of cell densities in different phases of the cell division cycle dependent on time t (hours) and an age-like variable a (hours) describing the time since arrival in a particular phase of the cell division cycle. The proposed structured model accounts for the essential in-host processes: parasite replication and its regulation by an antimalarial drug. The anti-malarial drug is incorporated in the model by an appropriate mathematical function and applied to a particular phase, namely, T-phase. The proposed cell transition and division intensity functions are capable of simulating near exponential parasite cell-mass growth (multiplication time of 48 days) while maintaining information regarding population age within each cell phase. Drug effect shows a significant parasite population reduction, leading to the recovery of malaria disease. Our simulation results also show that applying drug at T-phase might give the optimum reduction of parasitemia in the blood.   

11:00am-11:20am (Oct 1)
CLB 122
Shadi Heenatigala,
Texas Tech University

A Local Macroscopic Conservative (LoMaC) low-rank tensor method for the Vlasov Maxwell system
  The main computational challenges of solving the Vlasov-Maxwell (VM) system include the high dimensionality of the phase space, and inherent conservation properties, among others. In this paper, we develop a novel Local Macroscopic Conservative (LoMaC) low-rank tensor method for the VM system, as a continuation of our previous work (arXiv:2207.00518). Such a method employs the hierarchical Tuck decomposition to approximate the Vlasov solution tensor in high dimensions, mitigating the curse of dimensionality. Furthermore, the method simultaneously evolves the macroscopic conservation laws of mass, momentum, and energy using a flux-difference form with kinetic flux vector splitting alongside the Vlasov equation; then the LoMac property is realized by projecting the low-rank Vlasov solution onto a subspace that shares the same macroscopic observables by a conservative orthogonal projection. A collection of extensive numerical tests on the VM system are presented to demonstrate the algorithm's efficacy.

11:20am-11:40am (Oct 1)
CLB 122
Lu Zhang,
Columbia University

Coupling deep learning with full waveform inversion
  Full waveform inversion (FWI) aims at reconstructing unknown physical coefficients in wave equations using the wave field data generated from multiple incoming sources. In this work, we propose an offline-online computational strategy for coupling classical least-squares based computational inversion with modern deep learning based approaches for FWI to achieve advantages that can not be achieved with only one of the components. In a nutshell, we develop an offline learning strategy to construct a robust approximation to the inverse operator and utilize it to design a new objective function for the online inversion with new datasets. We demonstrate through numerical simulations that our coupling strategy improves the computational efficiency of FWI with reliable offline training on moderate computational resources (in terms of both the size of the training dataset and the computational cost needed).

11:40am-12:00pm (Oct 1)
CLB 122
Jannatul Ferdous Ema,
Texas Tech University

A new artificial viscosity approach for adaptive multiresolution discontinuous Galerkin method for hyperbolic conservation laws
  The adaptive multi-resolution discontinuous Galerkin (DG) method for hyperbolic conservation laws is proven effective in capturing the complex solutions structures when coupling a conventional artificial viscosity technique, while the computational cost is large due to the hierarchical structures of the multi-wavelet basis used. We propose a novel artificial viscosity approach for controlling spurious oscillations under the multi-resolution DG framework. In particular, the high order accuracy is not much compromised because the viscosity is added only for small scales of wavelet basis. This approach is easy to implement. The numerical evidence verifies the high order accuracy and the ability to control oscillations of the proposed approach.

3:10pm-3:30pm (Oct 1)
CLB 122

Yukun Yue,
Carnegie Mellon University
Convergence Analysis For A Semi-discrete Energy Stable Scheme For Hydrodynamic Q-tensor Model
  We present convergence analysis of an unconditional energy-stable first-order semi-discrete numerical scheme designed for a hydrodynamic Q-tensor model based on Invariant Quadratization Method(IEQ). This model couples a Navier-Stokes system for the flows and a parabolic type Q-tensor system governing the nematic crystal director fields. We prove the stability properties of the scheme and show convergence to weak solutions of the coupled liquid crystal system.

3:30pm-3:50pm (Oct 1)
CLB 122
Yasasya Batugedara Mohottalalage,
Michigan Technological University
Higher temporal accuracy for LES-C turbulent models
  Large Eddy Simulations (LES) are widely used in modeling turbulent flows. To reduce the modeling error in LES models, a method called Large Eddy Simulation with Correction (LES-C) was proposed in Labovsky(2020) using a 'predictor-corrector' scheme. To improve the model further by reducing the time discretization error, we propose a method that uses a defect-corrector scheme called Deferred correction. Since the method was obtained by adding additional terms to the LES -C model, we can obtain extra accuracy with no additional computational cost. The method is tested for the ADC model (a member of the LES -C family) and the full numerical test is carried out where a clear reduction of errors can be observed. We also performed the full numerical analysis of the method.

3:50pm-4:10pm (Oct 1)
CLB 122
Tianshi Lu,
Wichita State University

Melt pool formation by a moving heat source
  Rothensal solved the heat equation with a moving source analytically. Eagar and Tsai generalized the solution to Gaussian distributed heat sources. We extended their results to more general settings, and derived the asymptotic solution of a fast moving heat source. The results have been validated against simulations in the open-source CFD software OpenFOAM. We simulated the melting process of a metal block heated by a moving heat source, and compared the results with the prediction by the analytic solution to the heat equation. We also studied the melt pool formation in stacked metal beads heated by a moving laser beam, as in the Selective Laser Melting, the most advanced metal additive manufacturing process.

4:10pm-4:30pm (Oct 1)
CLB 122
Md Abu Helal,
Colorado State University

Optimal Ordering Policy For Forest Residues and Willow Biomass For Continuous Industrial Supply
  The development of biomass energy projects and other bio-based businesses depends on effective and efficient biomass logistics and supply from forestry and agricultural operations. Improved inventory management practices can contribute to increased competitive advantage and improved organizational performance in every industrial sector. Despite the potential direct and favorable influence of optimized inventory management on biomass supply chain efficiency, inventory management methods are often disregarded in the literature in this area. In this study we proposed an optimal inventory ordering policy for sustainable biomass supply chain management in the Mid-Atlantic region of the United States in order to improve biomass logistics to meet demand at the lowest possible cost and reduce risk to investment.