Computational Mathematics (CM)
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Exploring the link between coffee matrix microstructure and flow properties using combined X‐ray microtomography and smoothed particle hydrodynamics simulations
(2022-09-29)Coffee extraction involves many complex physical and transport processes extremely difficult to model. Among the many factors that will affect the final quality of coffee, the microstructure of the coffee matrix is one of ... -
Shape Optimization for Temperature Regulation in Extrusion Dies Using Microstructures
(2023-01-01)Plastic profile extrusion—a manufacturing process for continuous profiles with fixed cross section—requires a complex and iterative design process to prevent deformations and residual stresses in the final product. The ... -
Efficient Minimum Distance Computation for Solids of Revolution
(2020)We present a highly efficient algorithm for computing the minimum distance between two solids of revolution, each of which is defined by a planar cross-section region and a rotation axis. The boundary profile curve for ... -
Surface-Surface-Intersection Computation using a Bounding Volume Hierarchy with Osculating Toroidal Patches in the Leaf Nodes
(2022)We present an efficient and robust algorithm for computing the intersection curve of two freeform surfaces using a Bounding Volume Hierarchy (BVH), where the leaf nodes contain osculating toroidal patches. The covering ... -
A Review of a B-spline based Volumetric Representation: Design, Analysis and Fabrication of Porous and/or Heterogeneous Geometries
(2023)The needs of modern (additive) manufacturing (AM) technologies can no longer be satisfied by geometric modeling tools that are based on boundary representations (B-reps) - AM requires the representation and manipulation ... -
Implicit Functionally Graded Conforming Microstructures
(2023)The tensor product parametric representations are the most commonly used representation in geometric modeling. Yet, other representations have advantages in certain aspects, and in this work, we focus on employing implicit ... -
Conformal Parametric Microstructure Synthesis for Boundary Representations
(2022)The use of lattices and microstructures in geometric design have been recognized as potentially superior to solid structures due to the potential benefits in improved strength-to-weight ratios, better control over heat ... -
Euclidean Offset and Bisector Approximations of Curves over Freeform Surfaces
(2020)The computation of offset and bisector curves/surfaces has always been considered a challenging problem in geometric modeling and processing. In this work, we investigate a related problem of approximating offsets of ... -
Kernel-based Construction Operators for Boolean Sum and Ruled Geometry
(2023)Boolean sum and ruling are two well-known construction operators for both parametric surfaces and trivariates. In many cases, the input freeform curves in IR2 or surfaces in IR3 are complex, and as a result, these ... -
Conformal Microstructure Synthesis in Trimmed Trivariate based V-reps
(2021)We present a complete microstructure tiling paradigm for V-rep models, or volumetric models consisting of trimmed trivariates. Existing methods [10] are employed to tile individual primitive tensor product trivariates in ... -
Heterogeneous Parametric Trivariate Fillets
(2021)Blending and filleting are well established operations in solid modeling and computer-aided geometric design. The creation of a transition surface which smoothly connects the boundary surfaces of two (or more) objects has ... -
Self-Intersection Computation for Freeform Surfaces Based on a Regional Representation Scheme for Miter Points
(2021)We present an efficient and robust algorithm for computing the self-intersection of a freeform surface, based on a special representation of miter points, using sufficiently small quadrangles in the parameter domain. A ... -
Precise Hausdorff distance computation for freeform surfaces based on computations with osculating toroidal patches
(2021)We present an efficient algorithm for computing the precise Hausdorff Distance (HD) between two freeform surfaces. The algorithm is based on a hybrid Bounding Volume Hierarchy (BVH), where osculating toroidal patches (stored ... -
Synthesis of 3D jigsaw puzzles over freeform 2-manifolds
(2022)We present a simple algorithm for synthesizing 3D jigsaw puzzles from arbitrary 3D freeform 2-manifold geometric models represented with trimmed NURBS surfaces. The construction algorithm is based on a few conventional ... -
Fast parallel IGA-ADS solver for time-dependent Maxwell's equations
(2023-12)We propose a simulator for time-dependent Maxwell's equations with linear computational cost. We employ B-spline basis functions as considered in the isogeometric analysis (IGA). We focus on non-stationary Maxwell's equations ... -
Multimodal variational autoencoder for inverse problems in geophysics: application to a 1-D magnetotelluric problem
(2023-12)Estimating subsurface properties from geophysical measurements is a common inverse problem. Several Bayesian methods currently aim to find the solution to a geophysical inverse problem and quantify its uncertainty. However, ... -
Neural network architecture optimization using automated machine learning for borehole resistivity measurements
(2023-09)Deep neural networks (DNNs) offer a real-time solution for the inversion of borehole resistivity measurements to approximate forward and inverse operators. Using extremely large DNNs to approximate the operators is possible, ... -
Easy-to-implement hp-adaptivity for non-elliptic goal-oriented problems
(2023-11-29)The FEM has become a foundational numerical technique in computational mechanics and civil engineering since its inception by Courant in 1943 Courant1943. Originating from the Ritz method and variational calculus, the FEM ... -
Layer-Wise Learning Framework for Efficient DNN Deployment in Biomedical Wearable Systems
(2023-10)The development of low-power wearable systems requires specialized techniques to accommodate their unique requirements and constraints. While significant advancements have been made in the inference phase of artificial ...