Architecting the Finite Element Method Pipeline for the GPU.

The finite element method (FEM) is a widely employed numerical technique for approximating the solution of partial differential equations (PDEs) in various science and engineering applications. Many of these applications benefit from fast execution of the FEM pipeline. One way to accelerate the FEM pipeline is by exploiting advances in modern computational hardware, such as the many-core streaming processors like the graphical processing unit (GPU). In this paper, we present the algorithms and data-structures necessary to move the entire FEM pipeline to the GPU. First we propose an efficient GPU-based algorithm to generate local element information and to assemble the global linear system associated with the FEM discretization of an elliptic PDE. To solve the corresponding linear system efficiently on the GPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multi-grid (AMG) method preconditioner. We propose a new fine-grained parallelism strategy, a corresponding multigrid cycling stage and efficient data mapping to the many-core architecture of GPU. Comparison of our on-GPU assembly versus a traditional serial implementation on the CPU achieves up to an 87 × speedup. Focusing on the linear system solver alone, we achieve a speedup of up to 51 × versus use of a comparable state-of-the-art serial CPU linear system solver. Furthermore, the method compares favorably with other GPU-based, sparse, linear solvers.

RNF8-mediated multi-ubiquitination of MCM7: Linking disassembly of the CMG helicase with DNA damage response in human cells.

DNA damage causes genomic instability. To maintain genome integrity, cells have evolved DNA damage response, which is involved in replication fork disassembly and DNA replication termination. However, the mechanism underlying the regulation of replication fork disassembly and its connection with DNA damage repair remain elusive. The CMG-MCM7 subunit ubiquitination functions on the eukaryotic replication fork disassembly at replication termination. Until now, only ubiquitin ligases CUL2LRR1 have been reported catalyzing MCM7 ubiquitination in human cells. This study discovered that in human cells, the ubiquitin ligase RNF8 catalyzes K63-linked multi-ubiquitination of MCM7 at K145 both in vivo and in vitro. The multi-ubiquitination of MCM7 is dynamically regulated during the cell cycle, primarily presenting on chromatin during the late S phase. Additionally, MCM7 polyubiquitylation is promoted by RNF168 and BRCA1 during DNA replication termination. Upon DNA damage, the RNF8-mediated polyubiquitination of MCM7 decreased significantly during the late S phase. This study highlights the novel role of RNF8-catalyzed polyubiquitination of MCM7 in the regulation of replication fork disassembly in human cells and linking it to DNA damage response.

Photoenzymatic Decarboxylation to Produce Hydrocarbon Fuels: A Critical Review.

Photoenzymatic decarboxylation shows great promise as a pathway for the generation of hydrocarbon fuels. CvFAP, which is derived from Chlorella variabilis NC64A, is a photodecarboxylase capable of converting fatty acids into hydrocarbons. CvFAP is an example of coupling biocatalysis and photocatalysis to produce alkanes. The catalytic process is mild, and it does not yield toxic substances or excess by-products. However, the activity of CvFAP can be readily inhibited by several factors, and further enhancement is required to improve the enzyme yield and stability. In this article, we will examine the latest advancements in CvFAP research, with a particular focus on the enzyme's structural and catalytic mechanism, summarized some limitations in the application of CvFAP, and laboratory-level methods for enhancing enzyme activity and stability. This review can serve as a reference for future large-scale industrial production of hydrocarbon fuels.

PROPER ORDERED MESHING OF COMPLEX SHAPES AND OPTIMAL GRAPH CUTS APPLIED TO ATRIAL-WALL SEGMENTATION FROM DE-MRI.

Segmentation of the left atrium wall from delayed enhancement MRI is challenging because of inconsistent contrast combined with noise and high variation in atrial shape and size. This paper presents a method for left-atrium wall segmentation by using a novel sophisticated mesh-generation strategy and graph cuts on a proper ordered graph. The mesh is part of a template/model that has an associated set of learned intensity features. When this mesh is overlaid onto a test image, it produces a set of costs on the graph vertices which eventually leads to an optimal segmentation. The novelty also lies in the construction of proper ordered graphs on complex shapes and for choosing among distinct classes of base shapes/meshes for automatic segmentation. We evaluate the proposed segmentation framework quantitatively on simulated and clinical cardiac MRI.

A FAST ITERATIVE METHOD FOR SOLVING THE EIKONAL EQUATION ON TETRAHEDRAL DOMAINS.

Generating numerical solutions to the eikonal equation and its many variations has a broad range of applications in both the natural and computational sciences. Efficient solvers on cutting-edge, parallel architectures require new algorithms that may not be theoretically optimal, but that are designed to allow asynchronous solution updates and have limited memory access patterns. This paper presents a parallel algorithm for solving the eikonal equation on fully unstructured tetrahedral meshes. The method is appropriate for the type of fine-grained parallelism found on modern massively-SIMD architectures such as graphics processors and takes into account the particular constraints and capabilities of these computing platforms. This work builds on previous work for solving these equations on triangle meshes; in this paper we adapt and extend previous two-dimensional strategies to accommodate three-dimensional, unstructured, tetrahedralized domains. These new developments include a local update strategy with data compaction for tetrahedral meshes that provides solutions on both serial and parallel architectures, with a generalization to inhomogeneous, anisotropic speed functions. We also propose two new update schemes, specialized to mitigate the natural data increase observed when moving to three dimensions, and the data structures necessary for efficiently mapping data to parallel SIMD processors in a way that maintains computational density. Finally, we present descriptions of the implementations for a single CPU, as well as multicore CPUs with shared memory and SIMD architectures, with comparative results against state-of-the-art eikonal solvers.

Bayesian segmentation of atrium wall using globally-optimal graph cuts on 3D meshes.

Efficient segmentation of the left atrium (LA) wall from delayed enhancement MRI is challenging due to inconsistent contrast, combined with noise, and high variation in atrial shape and size. We present a surface-detection method that is capable of extracting the atrial wall by computing an optimal a-posteriori estimate. This estimation is done on a set of nested meshes, constructed from an ensemble of segmented training images, and graph cuts on an associated multi-column, proper-ordered graph. The graph/mesh is a part of a template/model that has an associated set of learned intensity features. When this mesh is overlaid onto a test image, it produces a set of costs which lead to an optimal segmentation. The 3D mesh has an associated weighted, directed multi-column graph with edges that encode smoothness and inter-surface penalties. Unlike previous graph-cut methods that impose hard constraints on the surface properties, the proposed method follows from a Bayesian formulation resulting in soft penalties on spatial variation of the cuts through the mesh. The novelty of this method also lies in the construction of proper-ordered graphs on complex shapes for choosing among distinct classes of base shapes for automatic LA segmentation. We evaluate the proposed segmentation framework on simulated and clinical cardiac MRI.

A FAST ITERATIVE METHOD FOR SOLVING THE EIKONAL EQUATION ON TRIANGULATED SURFACES.

This paper presents an efficient, fine-grained parallel algorithm for solving the Eikonal equation on triangular meshes. The Eikonal equation, and the broader class of Hamilton-Jacobi equations to which it belongs, have a wide range of applications from geometric optics and seismology to biological modeling and analysis of geometry and images. The ability to solve such equations accurately and efficiently provides new capabilities for exploring and visualizing parameter spaces and for solving inverse problems that rely on such equations in the forward model. Efficient solvers on state-of-the-art, parallel architectures require new algorithms that are not, in many cases, optimal, but are better suited to synchronous updates of the solution. In previous work [W. K. Jeong and R. T. Whitaker, SIAM J. Sci. Comput., 30 (2008), pp. 2512-2534], the authors proposed the fast iterative method (FIM) to efficiently solve the Eikonal equation on regular grids. In this paper we extend the fast iterative method to solve Eikonal equations efficiently on triangulated domains on the CPU and on parallel architectures, including graphics processors. We propose a new local update scheme that provides solutions of first-order accuracy for both architectures. We also propose a novel triangle-based update scheme and its corresponding data structure for efficient irregular data mapping to parallel single-instruction multiple-data (SIMD) processors. We provide detailed descriptions of the implementations on a single CPU, a multicore CPU with shared memory, and SIMD architectures with comparative results against state-of-the-art Eikonal solvers.