4,034 research outputs found
Hydrodynamics of Suspensions of Passive and Active Rigid Particles: A Rigid Multiblob Approach
We develop a rigid multiblob method for numerically solving the mobility
problem for suspensions of passive and active rigid particles of complex shape
in Stokes flow in unconfined, partially confined, and fully confined
geometries. As in a number of existing methods, we discretize rigid bodies
using a collection of minimally-resolved spherical blobs constrained to move as
a rigid body, to arrive at a potentially large linear system of equations for
the unknown Lagrange multipliers and rigid-body motions. Here we develop a
block-diagonal preconditioner for this linear system and show that a standard
Krylov solver converges in a modest number of iterations that is essentially
independent of the number of particles. For unbounded suspensions and
suspensions sedimented against a single no-slip boundary, we rely on existing
analytical expressions for the Rotne-Prager tensor combined with a fast
multipole method or a direct summation on a Graphical Processing Unit to obtain
an simple yet efficient and scalable implementation. For fully confined
domains, such as periodic suspensions or suspensions confined in slit and
square channels, we extend a recently-developed rigid-body immersed boundary
method to suspensions of freely-moving passive or active rigid particles at
zero Reynolds number. We demonstrate that the iterative solver for the coupled
fluid and rigid body equations converges in a bounded number of iterations
regardless of the system size. We optimize a number of parameters in the
iterative solvers and apply our method to a variety of benchmark problems to
carefully assess the accuracy of the rigid multiblob approach as a function of
the resolution. We also model the dynamics of colloidal particles studied in
recent experiments, such as passive boomerangs in a slit channel, as well as a
pair of non-Brownian active nanorods sedimented against a wall.Comment: Under revision in CAMCOS, Nov 201
Joint Reconstruction of Absorbed Optical Energy Density and Sound Speed Distribution in Photoacoustic Computed Tomography: A numerical Investigation
Photoacoustic computed tomography (PACT) is a rapidly emerging bioimaging
modality that seeks to reconstruct an estimate of the absorbed optical energy
density within an object. Conventional PACT image reconstruction methods assume
a constant speed-of-sound (SOS), which can result in image artifacts when
acoustic aberrations are significant. It has been demonstrated that
incorporating knowledge of an object's SOS distribution into a PACT image
reconstruction method can improve image quality. However, in many cases, the
SOS distribution cannot be accurately and/or conveniently estimated prior to
the PACT experiment. Because variations in the SOS distribution induce
aberrations in the measured photoacoustic wavefields, certain information
regarding an object's SOS distribution is encoded in the PACT measurement data.
Based on this observation, a joint reconstruction (JR) problem has been
proposed in which the SOS distribution is concurrently estimated along with the
sought-after absorbed optical energy density from the photoacoustic measurement
data. A broad understanding of the extent to which the JR problem can be
accurately and reliably solved has not been reported. In this work, a series of
numerical experiments is described that elucidate some important properties of
the JR problem that pertain to its practical feasibility. To accomplish this,
an optimization-based formulation of the JR problem is developed that yields a
non-linear iterative algorithm that alternatingly updates the two image
estimates. Heuristic analytic insights into the reconstruction problem are also
provided. These results confirm the ill-conditioned nature of the joint
reconstruction problem that will present significant challenges for practical
applications.Comment: 13 pages, submitted to IEEE Transactions on Computational Imagin
Tackling the Curse of Dimensionality with Physics-Informed Neural Networks
The curse-of-dimensionality (CoD) taxes computational resources heavily with
exponentially increasing computational cost as the dimension increases. This
poses great challenges in solving high-dimensional PDEs as Richard Bellman
first pointed out over 60 years ago. While there has been some recent success
in solving numerically partial differential equations (PDEs) in high
dimensions, such computations are prohibitively expensive, and true scaling of
general nonlinear PDEs to high dimensions has never been achieved. In this
paper, we develop a new method of scaling up physics-informed neural networks
(PINNs) to solve arbitrary high-dimensional PDEs. The new method, called
Stochastic Dimension Gradient Descent (SDGD), decomposes a gradient of PDEs
into pieces corresponding to different dimensions and samples randomly a subset
of these dimensional pieces in each iteration of training PINNs. We
theoretically prove the convergence guarantee and other desired properties of
the proposed method. We experimentally demonstrate that the proposed method
allows us to solve many notoriously hard high-dimensional PDEs, including the
Hamilton-Jacobi-Bellman and the Schr\"{o}dinger equations in thousands of
dimensions very fast on a single GPU using the PINNs mesh-free approach. For
example, we solve nontrivial nonlinear PDEs (the HJB-Lin equation and the BSB
equation) in 100,000 dimensions in 6 hours on a single GPU using SDGD with
PINNs. Since SDGD is a general training methodology of PINNs, SDGD can be
applied to any current and future variants of PINNs to scale them up for
arbitrary high-dimensional PDEs.Comment: 32 pages, 5 figure
A Framework for Megascale Agent Based Model Simulations on Graphics Processing Units
Agent-based modeling is a technique for modeling dynamic systems from the bottom up. Individual elements of the system are represented computationally as agents. The system-level behaviors emerge from the micro-level interactions of the agents. Contemporary state-of-the-art agent-based modeling toolkits are essentially discrete-event simulators designed to execute serially on the Central Processing Unit (CPU). They simulate Agent-Based Models (ABMs) by executing agent actions one at a time. In addition to imposing an un-natural execution order, these toolkits have limited scalability. In this article, we investigate data-parallel computer architectures such as Graphics Processing Units (GPUs) to simulate large scale ABMs. We have developed a series of efficient, data parallel algorithms for handling environment updates, various agent interactions, agent death and replication, and gathering statistics. We present three fundamental innovations that provide unprecedented scalability. The first is a novel stochastic memory allocator which enables parallel agent replication in O(1) average time. The second is a technique for resolving precedence constraints for agent actions in parallel. The third is a method that uses specialized graphics hardware, to gather and process statistical measures. These techniques have been implemented on a modern day GPU resulting in a substantial performance increase. We believe that our system is the first ever completely GPU based agent simulation framework. Although GPUs are the focus of our current implementations, our techniques can easily be adapted to other data-parallel architectures. We have benchmarked our framework against contemporary toolkits using two popular ABMs, namely, SugarScape and StupidModel.GPGPU, Agent Based Modeling, Data Parallel Algorithms, Stochastic Simulations
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