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Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large Scales

Periodic Reporting for period 4 - Big Splash (Big Splash: Efficient Simulation of Natural Phenomena at Extremely Large Scales)

Reporting period: 2019-09-01 to 2020-08-31

The main problem addressed by this project is the efficient simulation of large scale natural phenomena. Computer simulations of natural phenomena are essential in science, engineering, product design, shape modelling, and computer animation. Despite progress in algorithms and hardware, the simulation of large-scale natural phenomena is infeasible with current algorithms. In addition, simulations are typically iterated and tweaked until the desired output is produced; this type of interactive feedback loop is impossible with expensive simulations.

In this project, we view physics simulation methods from the perspective of computational complexity, and aim to use analytical transformations where possible to reduce the computational complexity and significantly increase the efficiency and scale of numerical simulation methods. We focus on simulation approaches for fluid dynamics (especially liquid simulation), fracture dynamics, and interactive techniques for editing and modifying existing simulations.

The overall goal of this project is to develop new algorithms for animating and simulating liquid and solid dynamics that require dramatically less computation than the state of the art. We hope to accomplish this goal by pursuing two main goals:
Goal 1: Develop efficient computational representations of natural phenomena inspired by closed-form solutions.
Goal 2: Develop algorithms for intelligently re-using existing simulation data.

We break these goals into four projects:
Project 1: Liquid Simulation, which investigates Airy wave theory, closed-form liquid surface waves, continuum simulation of bubbles and foam, and dimension reduction techniques.
Project 2: Fracture Simulation, which investigates Lagrangian crack fronts, ductile fracture and plasticity, detailed materials, and stress wavefronts.
Project 3: Space-time Manipulation, which investigates interpolating simulations, guiding simulations, editing time-dependent data, and compressing time-dependent data
Project 4: Efficient Re-simulation, which investigates a fundamental restructuring of the standard simulation workflow to only re-simulate where needed.
Project 1: Liquid Simulation
• Our research on liquid simulation has discovered several analytical reductions of the Navier-Stokes equations. Some highlights are a stream-function representations of bubbles and liquids (publications [4], [7], and [8]), analytical solutions of linear water wave theory (publications [9], [14], [16], [17], and [21]), and dimension-reduction approaches (publications [10], [11] and [19]).
• In total, the following publications resulted from this project: [1], [4], [7], [8], [9], [10], [11], [14], [16], [17], [18], [19], [21], [22], and [24].

Project 2: Fracture Simulation
• Our fracture simulation research generated two top-tier research publications based on analytical crack propagation and boundary elements (publications [2] and [6]).
• One PhD student based his dissertation on this topic and graduated in 2017 (publication [12]).
• Another group member simulated the shattering of complex fibrous assemblies by focusing on the break-up of anisotropic materials.
• In total, the following publications resulted from this project: [2], [6], [12], [20]

Project 3: Space-Time Manipulation
• Our research on blending liquids in space-time led to a publication focusing on interactive liquid simulation sculpting (publication [15]).
• In total, the following publication resulted from this project: [15]

Project 4: Efficient Re-Simulation
• Our research on non-reflecting boundary conditions using perfectly-matched layers resulted in the invention of a novel method for efficiently and locally re-simulating liquids (publication [3]).
• One PhD student based his dissertation on this topic and graduated in 2016 (publication [13]).
• Our research on numerical homogenization led to a top-tier publication based on the efficient re-simulation of fibrous materials like women and knitted cloth [23]
• In total, the following publications resulted from this project: [3],[13],[23]

Many of the publications resulting from this funding are at the top venue in the field, ACM SIGGRAPH.
Most of our results help to re-define the state of the art in liquid simulation and fracture simulation for computer graphics.

One main result of this project was the exploitation of boundary-based techniques to efficiently compute the most detailed fracture surfaces to date (publications [2], [6], [12]) and to simulate inviscid liquids with free surface boundary conditions without needing a volumetric discretization (publications [4], [7], [8], [14], [22]).

Another main result for liquid simulation is the use of Airy wave theory to redefine the state of the art in surface water wave simulation (publications [9], [14], [16], [17], [21], [24]). A third result for liquid simulation is the development of state of the art practical methods for large scale liquid simulations (like publications [10], [11], [18], [19]).

Although most of the progress was made on projects 1 and 2 (liquid and fracture simulation) we have also made progress towards our goals in projects 3 and 4 (space-time manipulation and re-simulation). Early steps toward space-time editing were published in [15], and our new technique for boundary handling redefined the state of the art in liquid re-simulation in [3], [13].

Finally, although the project has come to an end, we have just begun to explore new methods for significantly increasing the speed and realism when simulating complicated materials like woven and knitted cloth [23]. The techniques we have learned from this work inspired a number of follow-on projects, and the recent success of the work has led to a noticeable increase in career opportunities for the student author.