Related papers: Efficient multi-level hp-finite elements in arbitr…
We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the…
High Performance Computing (HPC) platforms allow scientists to model computationally intensive algorithms. HPC clusters increasingly use General-Purpose Graphics Processing Units (GPGPUs) as accelerators; FPGAs provide an attractive…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
Deep learning-based methods have shown remarkable effectiveness in solving PDEs, largely due to their ability to enable fast simulations once trained. However, despite the availability of high-performance computing infrastructure, many…
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…
This paper proposes a reinforcement learning framework for performance-driven structural design that combines bottom-up design generation with learned strategies to efficiently search large combinatorial design spaces. Motivated by the…
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…
Frameworks for the agile development of modern system-on-chips are crucial to dealing with the complexity of designing such architectures. The open-source Vespa framework for designing large, FPGA-based, multi-core heterogeneous…
A new formulation for the modular construction of flexible multibody systems is presented. By rearranging the equations for a flexible floating body and introducing the appropriate canonical momenta, the model is recast into a coupled…
We analyze a new framework for expressing finite element methods on arbitrarily many intersecting meshes: multimesh finite element methods. The multimesh finite element method, first presented in [40], enables the use of separate meshes to…
In this paper, we introduce the Phantom Domain Finite Element Method (PDFEM), a novel computational approach tailored for the efficient analysis of heterogeneous and composite materials. Inspired by fictitious domain methods, this method…
The use of composable abstractions allows the application of new and established algorithms to a wide range of problems while automatically inheriting the benefits of well-known performance optimisations. This work highlights the…
Since the seminal work of Idelsohn, O\~nate and Del-Pin (2004), the Particle Finite Element Method (PFEM) has relied on a Delaunay triangulation and the Alpha--Shape (AS) algorithm in the remeshing process. This approach guarantees a good…
We present FAST, an optimization framework for fast additive segmentation. FAST segments piecewise constant shape functions for each feature in a dataset to produce transparent additive models. The framework leverages a novel optimization…
The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having…
Research in efficient vision backbones is evolving into models that are a mixture of convolutions and transformer blocks. A smart combination of both, architecture-wise and component-wise is mandatory to excel in the speedaccuracy…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
A fundamental roadblock to the exact numerical solution of many-fermion problems is the exponential growth of the Hilbert space with system size. It manifests as extreme dynamical memory and computation-time requirements for simulating…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…