One forthcoming challenge in the area of high-performance computing is having the ability to run large-scale problems while coping with less memory per compute node. In this work, we investigate a novel data decomposition method that would allow Monte Carlo transport calculations to be performed on systems with limited memory per compute node. In this method, each compute node remotely retrieve...

This paper presents a method for finding cutting paths on a 3D triangular mesh surface to reduce the stretch in the flattened surface. The cutting paths link the surface boundary and the nodes where the Gaussian curvature is high, and their total length is minimized. First, a linear algorithm for computing an approximate boundary geodesic distance map is introduced; the map encapsulates the und...

For any graph G with fixed boundary there exists a layout in the plane, which minimizes the maximum Euclidean distance of any node to its neighbors. This layout balances the length of the graph edges and is therefore called a (length-) balanced layout of G. Furthermore the existence of a unique optimal balanced layout L with the following properties is proved: (i) L is the minimal element of an...

Monitoring the long-distance pipelines, rivers, roads and boundary lines with wireless sensor networks belongs to one-dimensional region monitoring. This paper primarily studies the coverage problems of the sensor networks in one-dimensional regions. Firstly, the onedimensional random coverage model is processed for the sensor nodes in one-dimensional monitoring region, and a formula is given t...

A new conserving approach in the context of Immersed Boundary Method (IBM) is presented to simulate one dimensional, incompressible flow in a moving boundary problem. The method employs control volume scheme to simulate the flow field. The concept of ghost node is used at the boundaries to conserve the mass and momentum equations. The Present methodimplements the conservation laws in all cells ...

The bounda y element method (BEM) is well suited for the electrostatic analysis of large, geometrically complex structures. When highly accurate solutions are required, the discretization (meshing) of the geometry becomes increasingly important. A scheme is required to construct optimal meshes, in the sense that maximum accuracy of the solution can be achieved with minimal computational eflort....

This study proposes a novel heterogeneous graph convolutional neural network (HGCNN) to handle complex brain fMRI data at regional and across-region levels. We introduce generic formulation of spectral filters on graphs by introducing the $$k-th$$ Hodge-Laplacian (HL) operator. In particular, we propose Laguerre polynomial approximations HL prove that their spatial localization is related order...

Wireless Sensor Networks (WSNs) plays an important role for monitoring strategic and dangerous hi security sites. Failure of some sensor nodes can lead to a failure of hole system which causes losses such as economical, equipment damage and even risks for human lives. Moreover, failures are unavoidable in WSNs due to hardware constraints, hostile environment, unattended deployment and limited r...

In this paper, we derive a family of source term quadrature formulas for preserving third-order accuracy of the node-centered edge-based discretization for conservation laws with source terms on arbitrary simplex grids. A three-parameter family of source term quadrature formulas is derived, and as a subset, a oneparameter family of economical formulas is identified that does not require second ...

The paper reports an efficient and fully parallel 2D shape recognition method based on the use of a multiscale tree representation of the shape boundary and recursive learning of trees. Specifically, the shape is represented by means of a tree where each node, corresponding to a boundary segment at some level of resolution, is characterized by a real vector containing curvature, length, symmetr...