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In this work, a recently developed fracture modeling method called localizing gradient damage method (LGDM) is implemented in MATLAB. MATLAB is well-known in the computational research community for its simple and easy-to-learn coding…
Heterogeneous computing and exploiting integrated CPU-GPU architectures has become a clear current trend since the flattening of Moore's Law. In this work, we propose a numerical and algorithmic re-design of a p-adaptive quadrature-free…
Graphics Processing Unit (GPU) computing is becoming an alternate computing platform for numerical simulations. However, it is not clear which numerical scheme will provide the highest computational efficiency for different types of…
In this paper we provide some Matlab tools for efficient vectorized coding of the Hybridizable Discontinuous Galerkin for linear variable coefficient reaction-diffusion problems in polyhedral domains. The resulting tools are modular and…
We present a novel implementation of the modal discontinuous Galerkin (DG) method for hyperbolic conservation laws in two dimensions on graphics processing units (GPUs) using NVIDIA's Compute Unified Device Architecture (CUDA). Both…
We present a high order time-domain nodal discontinuous Galerkin method for wave problems on hybrid meshes consisting of both wedge and tetrahedral elements. We allow for vertically mapped wedges which can be deformed along the extruded…
This paper develops a high-order selective discontinuous Galerkin (SDG) method for solving elliptic interface problems on interface-unfitted Cartesian meshes. This method applies the discontinuous Galerkin (DG) formulation on interface…
The discontinuous Galerkin (DG) finite element method is conservative, lends itself well to parallelization, and is high-order accurate due to its close affinity with the theory of quadrature and orthogonal polynomials. When applied with an…
High-order accurate discontinuous Galerkin (DG) methods have emerged as powerful tools for solving partial differential equations such as the compressible Navier-Stokes equations due to their excellent dispersion-dissipation properties and…
In this paper, we propose a method for constructing a neural network viscosity in order to reduce the non-physical oscillations generated by high-order Discontiuous Galerkin (DG) methods. To this end, the problem is reformulated as an…
This paper introduces a code generator designed for node-level optimized, extreme-scalable, matrix-free finite element operators on hybrid tetrahedral grids. It optimizes the local evaluation of bilinear forms through various techniques…
We present a new class of iterative schemes for solving initial value problems (IVP) based on discontinuous Galerkin (DG) methods. Starting from the weak DG formulation of an IVP, we derive a new iterative method based on a preconditioned…
The proximal Galerkin finite element method is a high-order, low-iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of point-wise bound constraints in infinite-dimensional function spaces.…
This paper is concerned with developing accurate and efficient numerical methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in multiple spatial dimensions. It presents a general framework…
Generating high-quality Scalable Vector Graphics (SVGs) from text remains a significant challenge. Existing LLM-based models that generate SVG code as a flat token sequence struggle with poor structural understanding and error accumulation,…
Creating scalable, high performance PDE-based simulations requires a suitable combination of discretizations, differential operators, preconditioners and solvers. The required combination changes with the application and with the available…
This paper proposes a matrix-free residual evaluation technique for the hybridizable discontinuous Galerkin method requiring a number of operations scaling only linearly with the number of degrees of freedom. The method results from…
Vectorization is increasingly important to achieve high performance on modern hardware with SIMD instructions. Assembly of matrices and vectors in the finite element method, which is characterized by iterating a local assembly kernel over…
This is the first in a series of papers on implementing a discontinuous Galerkin method as a MATLAB / GNU Octave toolbox. The main goal is the development of techniques that deliver optimized computational performance combined with a…
In this work, we propose a novel strategy for the numerical solution of linear convection diffusion equation (CDE) over unfitted domains. In the proposed numerical scheme, strategies from high order Hybridized Discontinuous Galerkin method…