Doctoral Defense - Bryce Palmer

About the Event

The Department of Mechanical Engineering
Michigan State University

Ph.D. Dissertation Defense
Thursday, July 10, 2025 at 2:00 PM EDT
Remote via Zoom
https://simonsfoundation.zoom.us/j/92937215459
Password: Contact Department or Advisor for Zoom Password

ABSTRACT

ON THE LARGE-SCALE SIMULATION OF MULTIBODY NONLOCAL DYNAMICS

By: Bryce Palmer
Advisor: Dr. Tong Gao

This dissertation targets the large-scale simulation of multibody nonlocal dynamics (MND): systems of rigid or flexible bodies interconnected by springs, hinges, joints, or motors, and fully coupled through long-range effects—such as hydrodynamic, electromagnetic, or gravitational interactions—that transmit forces through a shared medium and induce motion across distance. Unlike the robotic and mechanical assemblies central to classical multibody dynamics, MND systems arise predominantly in microbiology and biophysics and include examples such as fiber networks, cell colonies, and intracellular structures. These systems also differ in kind: they are living. Bodies may grow, shrink, divide, and die; they may consume nutrients to self-propel or to drive the dynamic formation and dissolution of bonds. Interactions may encode biochemical communication—not just mechanical force. Such features place unique demands on algorithms, data structures, and computational abstractions. The evolving nature of connectivity stands in stark contrast to the fixed topologies of engines or robotic arms. At the same time, the presence of long-range interactions shifts the dominant computational burden from neighbor detection and constraint resolution to the evaluation of dense, nonlocal couplings, rendering many fast algorithms developed for classical multibody dynamics ineffective or inapplicable.

Classical multibody dynamics has excelled at identifying shared structure across seemingly disparate mechanical systems—robotic arms, engines, spacecraft assemblies—and transforming those abstractions into robust, general-purpose infrastructure. Over decades, this has produced libraries whose layered complexity far exceeds what any single developer could achieve. But these tools are built around assumptions—fixed connectivity, inertial motion, pointlike particles, localized interactions—that are fundamentally incompatible with the biologically grounded, structure-evolving, and nonlocally coupled systems that define MND. These domain-specific assumptions are deeply embedded and difficult to circumvent without substantial rewrites.

As a result, the software landscape for multibody nonlocal dynamics remains fractured. Each application domain—bacterial colonies, cytoskeletal networks, red blood cells—relies on its own bespoke codebase, with siloed algorithms, incompatible data layouts, and limited interoperability. Improvements in one domain are difficult translate to another, increasing development time and stalling progress toward larger, more realistic simulations. Yet there is no fundamental reason why MND cannot achieve the same level of infrastructure reuse and algorithmic generality as classical multibody dynamics. Doing so requires new abstractions, algorithms, and software design principles tuned to the unique character these systems. The work that follows advances this agenda along three complementary fronts: algorithm development, infrastructure-level software design, and the application of these tools to biophysical systems at scales and fidelities previously unattainable.

From the algorithmic side, we introduce the Recursively generated Linear Complementarity Problem (ReLCP), a collision resolution algorithm designed to reduce the number of long-range interaction evaluations in densely packed, non-spherical systems. These evaluations can dominate the cost of multibody nonlocal dynamics, particularly when the numerical stiffness of potential-based collision handling necessitates excessively small timesteps or when optimization-based methods take many iterations to converge. While optimization approaches offer robustness over potential-based schemes, their performance for smooth, non-spherical bodies has been limited by the poor scalability of discrete surface representations. Such methods approximate geometry using tessellations or rigid sub-objects, often oversampling surfaces to preserve fidelity—resulting in excessively large numbers of constraints. ReLCP avoids this overhead by replacing static surface discretization with a recursive constraint-generation scheme. Starting with a single constraint per near-contact pair, it adaptively introduces new contact points only where unconstrained motion would otherwise lead to overlap. This approach preserves the accuracy of smooth-surface interactions while reducing constraint count—and with it, the number of costly force evaluations—by one to two orders of magnitude. We establish conditions for existence, uniqueness, and convergence to the underlying continuous-time dynamics. The resulting algorithm achieves 10–100× speedups and enables large-scale simulations in regimes previously inaccessible to classical methods.

On the infrastructure side, we introduce MuNDy, a modular, high-performance simulation library purpose-built for the demands of multibody nonlocal dynamics. MuNDy targets a fragmented landscape—where tools for cell colonies, cytoskeletal networks, and colloidal suspensions have historically evolved in isolation—working toward a unifying, extensible framework capable of supporting heterogeneous particles, dynamic connectivity, and long-range interactions across domains. Built atop Sandia National Lab's Sierra ToolKit Mesh (STK), MuNDy adds a lightweight mathematics library, type-safe component model that decouples memory layout from algorithmic logic, streamlined user interface, and GPU-compatible dynamic connectivity infrastructure. It provides domain-specific capabilities essential for nonlocal simulation, including GPU-compatible boundary integral solvers, fast multipole support, and direct kernel evaluation with coalesced memory access. Benchmarks of MuNDy’s contact resolution algorithm show up to 1000× speedup over aLENS—an MPI/OpenMP-based library implementing the same algorithm—by leveraging GPU acceleration and improved scalability. MuNDy's performance matched that of a hand-optimized Kokkos version restricted to homogeneous spheres, demonstrating that the flexibility of STK's runtime extensible heterogeneity and subset selectability do not inhibit performance. Though currently in beta release, MuNDy has already been deployed adopted in multiple simulation studies, with early user feedback guiding improvements to interface design, missing features, and performance bottlenecks. This iterative model reflects the broader aim of this thesis: to establish the architectural foundation for scalable, reusable infrastructure in biologically grounded multibody simulation.

The tools developed herein enable four original scientific studies, each resulting in a peer-reviewed publication. These are not merely validations of the infrastructure, but full-scale investigations that yield novel insights, advance domain knowledge, and demonstrate the versatility and scalability of the framework. Spanning active nematics, crowded suspensions, proliferating colonies, and densely packed ciliated media, these studies underscore the unifying power of multibody nonlocal dynamics to tackle diverse, biologically grounded systems through shared abstractions and reusable infrastructure.