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Computationally modeling the laser powder bed fusion process can be expensive despite the fact that the laser covers a small fraction of the entire domain. Hence, we developed GO-MELT, a multilevel approach inspired by the variational multiscale method. GO-MELT calculates the full temperature solution using three coupled thermal solvers, each solving one of three overlapping domains, subsequently referred to as levels. Level 1's solver obtains a global, coarse-scale solution. Level 2's solver computes a meso-scale thermal field spanning the melt pool region. Level 3's solver obtains a fine-scale temperature field spanning the laser's immediate region. Coarser solutions provide boundary conditions for finer solvers. Finer solutions compute subgrid scales that influence coarser solvers through additional source terms. Being independently meshed, Levels 2 and 3 can track a laser along its tool path without remeshing. Moreover, fixed-sized, structured meshes allow for GPU acceleration using Google's JAX library with just-in-time compilation. Five case studies were conducted to demonstrate proper convergence of GO-MELT, to show that GO-MELT can reach the same accuracy as a uniform mesh with fewer degrees of freedom, and to quantify the computational load from each level's solver. A simulated production run averaged 1.64 ms per time step after taking 9.36 h to complete 20.5 million time steps, which is approximately 678 × faster than a uniform mesh solver with identical resolution and GPU acceleration. Future work will implement different solvers into GO-MELT to improve fidelity and speed. [Display omitted] • Developed multiscale framework inspired by VMS to combine separate thermal solvers. • Integrated GPU acceleration in Python using Google's JAX library with JIT compilation. • Simulated LPBF printing a 10 mm cube (20.5 million time steps) in 9.36 h. • Achieved 678x speedup compared to a uniform mesh of the same resolution. [ABSTRACT FROM AUTHOR]

This paper presents a general Convolution Hierarchical Deep-learning Neural Networks (C-HiDeNN) computational framework for solving partial differential equations. This is the first paper of a series of papers devoted to C-HiDeNN. We focus on the theoretical foundation and formulation of the method. The C-HiDeNN framework provides a flexible way to construct high-order C n approximation with arbitrary convergence rates and automatic mesh adaptivity. By constraining the C-HiDeNN to build certain functions, it can be degenerated to a specification, the so-called convolution finite element method (C-FEM). The C-FEM will be presented in detail and used to study the numerical performance of the convolution approximation. The C-FEM combines the standard C 0 FE shape function and the meshfree-type radial basis interpolation. It has been demonstrated that the C-FEM can achieve arbitrary orders of smoothness and convergence rates by adjusting the different controlling parameters, such as the patch function dilation parameter and polynomial order, without increasing the degrees of freedom of the discretized systems, compared to FEM. We will also present the convolution tensor decomposition method under the reduced-order modeling setup. The proposed methods are expected to provide highly efficient solutions for extra-large scale problems while maintaining superior accuracy. The applications to transient heat transfer problems in additive manufacturing, topology optimization, GPU-based parallelization, and convolution isogeometric analysis have been discussed. [ABSTRACT FROM AUTHOR]

Metal powder-based Additive Manufacturing (AM) processes are increasingly used in industry and science due to their unique capability of building complex geometries. However, the immense computational cost associated with AM predictive models hinders the further industrial adoption of these technologies for time-sensitive applications, process design with uncertainties or real-time process control. In this work, a novel approach to accelerate the explicit finite element analysis of the transient heat transfer of AM processes is proposed using Graphical Processing Units. The challenges associated with this approach are enumerated and multiple strategies to overcome each challenge are discussed. The performance of the proposed algorithms is evaluated on multiple test cases. Speed-ups of about 100 ×–150 × compared to an optimized single CPU core implementation for the best strategy were achieved. [ABSTRACT FROM AUTHOR]