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Robust, broadly applicable fluid-structure interaction (FSI) algorithms remain a challenge for computational mechanics. In previous work, we introduced an immersed interface method (IIM) for discrete surfaces and an extension based on an…
Density matrix embedding theory (DMET) is a quantum embedding theory for strongly correlated systems. From a computational perspective, one bottleneck in DMET is the optimization of the correlation potential to achieve self-consistency,…
In this work we present a novel computational method for embedding arbitrary curved one-dimensional (1D) fibers into three-dimensional (3D) solid volumes, as e.g. in fiber-reinforced materials. The fibers are explicitly modeled with highly…
Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared to…
Partitionings (or segmentations) divide a given domain into disjoint connected regions whose union forms again the entire domain. Multi-dimensional partitionings occur, for example, when analyzing parameter spaces of simulation models,…
In many applications, thin shell-like structures are integrated within or attached to volumetric bodies. This includes reinforcements placed in soft matrix material in lightweight structure design, or hollow structures that are partially or…
Multimodal tasks, such as image-text retrieval and generation, require embedding data from diverse modalities into a shared representation space. Aligning embeddings from heterogeneous sources while preserving shared and modality-specific…
A discrete conformality for polyhedral metrics on surfaces is introduced in this paper which generalizes earlier work on the subject. It is shown that each polyhedral metric on a surface is discrete conformal to a constant curvature…
With the increase in computational power for the available hardware, the demand for high-resolution data in computer graphics applications increases. Consequently, classical geometry processing techniques based on linear algebra solutions…
Reconstructing surfaces from normals is a key component of photometric stereo. This work introduces an adaptive surface triangulation in the image domain and afterwards performs the normal integration on a triangle mesh. Our key insight is…
We introduce an algorithm to remesh triangle meshes representing developable surfaces to planar quad dominant meshes. The output of our algorithm consists of planar quadrilateral (PQ) strips that are aligned to principal curvature…
Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly…
We determine the local geometric structure of two-dimensional metric spaces with curvature bounded above as the union of finitely many properly embedded/branched immersed Lipschitz disks. As a result, we obtain a graph structure of the…
Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted…
Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…
The question of representation of 3D geometry is of vital importance when it comes to leveraging the recent advances in the field of machine learning for geometry processing tasks. For common unstructured surface meshes state-of-the-art…
Applications that require Internet access to remote 3D datasets are often limited by the storage costs of 3D models. Several compression methods are available to address these limits for objects represented by triangle meshes. Many CAD and…
This paper introduces a general modeling framework for a multi-type maximal covering location problem in which the position of facilities in different metric spaces are simultaneously decided to maximize the demand generated by a set of…
An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh deformation technique (MDT) used to adapt the computational mesh in the moving fluid domain. An ideal technique is computationally…
This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order…