Complex Geometries
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Related Articles from SNS
Four-Level Overlapping Schwarz as Multigrid Coarse Solver for Incompressible Non-Newtonian Flow in Complex Geometries
arXiv:2606.01433v1 Announce Type: new Abstract: For complex geometries, the coarse problem of geometric multigrid can be too large to be solved by a direct solver. Here, we report on the use of domain decomposition applied to the multigrid coarse problem. Additive overlapping Schwarz methods are domain decomposition methods for the iterative solution of partial differential equations whose numerical and parallel scalability can be improved by the addition of coarse levels.
Compatibility and Accuracy Verification of CADmesh-Based Complex Geometry Modeling in Geant4
arXiv:2606.06508v1 Announce Type: new Abstract: Geant4 Monte Carlo simulation relies on the Constructive Solid Geometry (CSG) method for complex geometric modeling. This method has low efficiency and a high application threshold. Importing triangular facet formats such as STL/OBJ via CADmesh is a promising alternative, but systematic evaluations of format compatibility, geometric accuracy, and physical simulation deviations are lacking.
Hidden geometry explains why kernel methods separate complex data so well
Hidden geometry explains why kernel methods separate complex data so well Lisa Lock Scientific Editor Robert Egan Associate Editor Are two sets of data genuinely different, or is it because of randomness? This question, known as the two-sample testing problem, becomes notoriously difficult in modern datasets, because they are often high-dimensional, complex, and differences between them can take countless subtle forms. "Simply put, we don't know what differences to look for, the...
Tensor Network Lattice Boltzmann Method for Data-Compressed Fluid Simulations
Announce Type: replace Abstract: Resolving unsteady transport phenomena in geometrically complex domains is traditionally constrained by polynomial scaling of computational cost with spatial resolution. While methods based on tensor-network data representations or matrix-product states (MPS) data encodings have emerged as a technique to systematically reduce degrees of freedom, existing formulations do not extend to complex geometries and complex flow physics. Both capabilities are offered...
A scalable Ewald-free BIE framework for periodic Stokes flow via hierarchical proxy sums
arXiv:2605.30805v1 Announce Type: cross Abstract: Particulate Stokes flow in confined, periodic geometries underlies a broad class of problems in biophysics, microfluidics, and the rheology of complex fluids. Boundary integral equation (BIE) methods are a natural tool for such problems, but existing periodization schemes rely either on periodic Green's functions, which are restrictive for complex confining geometries, or on free-space schemes that solve auxiliary proxy strengths alongside...
A scalable Ewald-free BIE framework for periodic Stokes flow via hierarchical proxy sums
arXiv:2605.30805v1 Announce Type: new Abstract: Particulate Stokes flow in confined, periodic geometries underlies a broad class of problems in biophysics, microfluidics, and the rheology of complex fluids. Boundary integral equation (BIE) methods are a natural tool for such problems, but existing periodization schemes rely either on periodic Green's functions, which are restrictive for complex confining geometries, or on free-space schemes that solve auxiliary proxy strengths alongside the...
SBP-Net: Learning Thin Structure Reconstruction with Sliding-Box Projections
Announce Type: new Abstract: Reconstructing thin 3D structures is challenging due to their sparsity, scale variation, and complex geometry. Such structures arise in a wide range of domains, including medical imaging of vascular systems and industrial pipe systems. While recent neural methods perform well on dense surfaces, they often fail to recover fine thin geometries.
Exploring Neural Network Surrogates for High-Order Mesh-Free Interpolants
arXiv:2503.23230v3 Announce Type: replace Abstract: Mesh-free numerical methods offer flexibility in the discretisation of complex geometries, showing significant potential for problems where mesh-based methods struggle. Although high-order approximations can be obtained through consistency-correction linear systems, such approaches remain prohibitively expensive for Lagrangian formulations, which commonly exhibit low-order convergence. Here we investigate the use of machine learning (ML) to...
A fast and consistent sharp-interface immersed boundary method for moving bodies of arbitrary thicknes
arXiv:2606.09799v1 Announce Type: new Abstract: Immersed boundary methods (IBMs) are widely used to simulate flows around complex geometries and moving bodies, but they often involve a trade-off between precision and computational efficiency. Eulerian formulations require special treatments for moving walls and may generate spurious force oscillations, whereas Lagrangian formulations can suffer from slip errors at the immersed surfaces. We propose a novel sharp-interface IBM for...
Cubic Hermite Lattice Structures
arXiv:2606.06500v1 Announce Type: new Abstract: Lattice structures are of growing importance in additive manufacturing, where complex internal geometries are increasingly required for lightweight, high surface-to-volume ratios, multifunctionality, and other superior mechanical properties. Conventional lattice modeling methods typically represent struts with simple primitives, such as cylinders or cones, limiting geometric diversity and the design space.