This thesis presents a scalable, high-resolution simulation framework for a reaction diffusion prey-predator model with finite hunting ranges. The model’s integral predation term produces stiff, non-local dynamics that present a challenge to traditional explicit or fully implicit solvers. This study overcome this barrier by incorporating a third-order Krylov Subspace Spectral (KSS) time integrator into a Fourier spectral spatial discretization. KSS, which treats each Fourier mode with a frequency-dependent polynomial, avoids the need for solutions of large linear systems in implicit schemes and maintains the computing simplicity of explicit schemes. It also allows for larger time steps compared to stability-limited Runge-Kutta methods. Benchmarking KSS against LEJA interpolation and Adaptive Krylov-Projection (AKP) exponential integrators on grids up to N = 8000 shows it maintains a constant iteration count of four Fast fourier tranforms (FFTs) per iteration, achieves relative errors below 10−8 and delivers result up to 40 times faster. Large-scale simulations show a variety of spatial and temporal behaviors, including stationary prey refuges, periodic and aperiodic traveling waves, and regime coexistence. These findings support and expand prior analytical predictions for non-local predation.
","abstract_html":"<p>This thesis presents a scalable, high-resolution simulation framework for a reaction diffusion prey-predator model with finite hunting ranges. The model’s integral predation term produces stiff, non-local dynamics that present a challenge to traditional explicit or fully implicit solvers. This study overcome this barrier by incorporating a third-order Krylov Subspace Spectral (KSS) time integrator into a Fourier spectral spatial discretization. KSS, which treats each Fourier mode with a frequency-dependent polynomial, avoids the need for solutions of large linear systems in implicit schemes and maintains the computing simplicity of explicit schemes. It also allows for larger time steps compared to stability-limited Runge-Kutta methods. Benchmarking KSS against LEJA interpolation and Adaptive Krylov-Projection (AKP) exponential integrators on grids up to N = 8000 shows it maintains a constant iteration count of four Fast fourier tranforms (FFTs) per iteration, achieves relative errors below 10−8 and delivers result up to 40 times faster. Large-scale simulations show a variety of spatial and temporal behaviors, including stationary prey refuges, periodic and aperiodic traveling waves, and regime coexistence. These findings support and expand prior analytical predictions for non-local predation.</p>","abstract_has_math":false,"creators":["Hackman, Emmanuel"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Dr. James Lambers","Dr. Qingguang Guan","Dr. Huiquing Zhu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-08-01T07:00:00Z","date_published":"2025-08-01T07:00:00Z","updated_at":"2026-07-24T05:45:55Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/1145","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dr. James Lambers","Dr. Qingguang Guan","Dr. Huiquing Zhu"]},{"key":"dc:creator","label":"Author","values":["Hackman, Emmanuel"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2027-08-01T07:00:00Z"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/1145"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis presents a scalable, high-resolution simulation framework for a reaction diffusion prey-predator model with finite hunting ranges. The model’s integral predation term produces stiff, non-local dynamics that present a challenge to traditional explicit or fully implicit solvers. This study overcome this barrier by incorporating a third-order Krylov Subspace Spectral (KSS) time integrator into a Fourier spectral spatial discretization. KSS, which treats each Fourier mode with a frequency-dependent polynomial, avoids the need for solutions of large linear systems in implicit schemes and maintains the computing simplicity of explicit schemes. It also allows for larger time steps compared to stability-limited Runge-Kutta methods. Benchmarking KSS against LEJA interpolation and Adaptive Krylov-Projection (AKP) exponential integrators on grids up to N = 8000 shows it maintains a constant iteration count of four Fast fourier tranforms (FFTs) per iteration, achieves relative errors below 10−8 and delivers result up to 40 times faster. Large-scale simulations show a variety of spatial and temporal behaviors, including stationary prey refuges, periodic and aperiodic traveling waves, and regime coexistence. These findings support and expand prior analytical predictions for non-local predation.
"]},{"key":"dc:title","label":"Title","values":["Scalable High-Resolution Simulation of the Prey-Predator Model, with a Non-Local Consumption of Prey"]}]}],"canonical_facts":{"dc:contributor":["Dr. James Lambers","Dr. Qingguang Guan","Dr. Huiquing Zhu"],"dc:creator":["Hackman, Emmanuel"],"dc:date.available":["2027-08-01T07:00:00Z"],"dc:description.abstract":["This thesis presents a scalable, high-resolution simulation framework for a reaction diffusion prey-predator model with finite hunting ranges. The model’s integral predation term produces stiff, non-local dynamics that present a challenge to traditional explicit or fully implicit solvers. This study overcome this barrier by incorporating a third-order Krylov Subspace Spectral (KSS) time integrator into a Fourier spectral spatial discretization. KSS, which treats each Fourier mode with a frequency-dependent polynomial, avoids the need for solutions of large linear systems in implicit schemes and maintains the computing simplicity of explicit schemes. It also allows for larger time steps compared to stability-limited Runge-Kutta methods. Benchmarking KSS against LEJA interpolation and Adaptive Krylov-Projection (AKP) exponential integrators on grids up to N = 8000 shows it maintains a constant iteration count of four Fast fourier tranforms (FFTs) per iteration, achieves relative errors below 10−8 and delivers result up to 40 times faster. Large-scale simulations show a variety of spatial and temporal behaviors, including stationary prey refuges, periodic and aperiodic traveling waves, and regime coexistence. These findings support and expand prior analytical predictions for non-local predation.
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/1145"],"dc:title":["Scalable High-Resolution Simulation of the Prey-Predator Model, with a Non-Local Consumption of Prey"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:45:55Z"}