Pochoir is a compiler for a domain-specific language embedded in C++ which produces excellent code from a simple specification of a desired stencil computation. Pochoir allows a wide variety of boundary conditions to be specified, and it automatically parallelizes and optimizes cache performance. Benchmarks of Pochoir-generated code demonstrate a performance advantage of 2–10 times over standar...

We propose an original approach called “stencil-masked ion implantation process” to perform a spatially localized synthesis of a limited number of Si nanoparticles (nps) within a thin SiO 2 layer. This process consists in implanting silicon ions at ultra-low energy through a stencil mask containing a periodic array of opened windows (from 50 nm to 2 μm). After the stencil removal, a thermal ann...

We present a Ritz-Galerkin discretization on sparse grids using pre-wavelets, which allows to solve elliptic differential equations with variable coefficients for dimension d = 2, 3 and higher dimensions d > 3. The method applies multilinear finite elements. We introduce an efficient algorithm for matrix vector multiplication using a Ritz-Galerkin discretization and semi-orthogonality. This alg...

This paper fully develops Diamond Tiling, a technique to partition the computations of stencil applications such as FDTD. The Diamond Tiling technique is the result of optimizing the amount of useful computations that can be executed when a region of memory is loaded to the local memory of a multiprocessor chip. Diamond Tiling contributes to the state of the art on time tiling techniques in tha...

Many biological processes, such as stem cell differentiation, wound healing and development, involve dynamic interactions between cells and their microenvironment. The ability to control these dynamic processes in vitro would be potentially useful to fabricate tissue engineering constructs, study biological processes, and direct stem cell differentiation. In this paper, we used a parylene-C mic...

Efficient frequency-domain full-waveform inversion (FWI) of long-offset node data can be designed with a few discrete frequencies, which lead to modest volumes managed during the process. Moreover, attenuation effects straightforwardly implemented in forward problem without computational overhead. However, 3D seismic modeling is challenging because it requires solving large and sparse linear in...

Application codes reliably achieve performance far less than the advertised capabilities of existing architectures, and this problem is worsening with increasingly-parallel machines. For large-scale numerical applications, stencil operations are often impose the greater part of the computational cost, and the primary sources of ineeciency are the costs of message passing and poor cache utilizat...

Stencil-based kernels constitute the core of many important scientific applications on blockstructured grids. Unfortunately, these codes achieve a low fraction of peak performance, due primarily to the disparity between processor and main memory speeds. In this paper, we explore the impact of trends in memory subsystems on a variety of stencil optimization techniques and develop performance mod...

We focus on linear systems stemming from discretization of PDEs. The non-zero structure of matrices of such systems depends on the discretized domain and the stencil in use. Analyzing parallel communication for an arbitraty problem seems unfeasible. Thus, we are dealing with a model problem: a square k-by-k mesh and a 5-point stencil. Presumably, the results for other stencils using the same me...

We present a generalization of the RBF-FD method that allows full control of the overlap between RBF-FD stencils. We accomplish this by introducing a continuous overlap parameter δ ∈ [0, 1] such that δ = 1 recovers the standard RBF-FD method and δ = 0 results in a full decoupling of the RBF-FD stencils. We show with a simple example that global interpolation with both RBFs and RBFs augmented wi...