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For many applications, we need to use techniques to represent convex shapes and objects. In this work, we use level set method to represent shapes and find a necessary and sufficient condition on the level set function to guarantee the…
Level set-based immersed boundary techniques operate on nonconforming meshes while providing a crisp definition of interface and external boundaries. In such techniques, an isocontour of a level set field interpolated from nodal level set…
The macroscopic properties of materials that we observe and exploit in engineering application result from complex interactions between physics at multiple length and time scales: electronic, atomistic, defects, domains etc. Multiscale…
We extend thresholding methods for numerical realization of mean curvature flow on obstacles to the anisotropic setting where interfacial energy depends on the orientation of the interface. This type of schemes treats the interface…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…
Obtaining a rigorous and reliable method for linking computer simulations of polymer blends and composites at different length scales of interest is a highly desirable goal in soft matter physics. In this paper a multiscale modeling…
This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of…
Recent advancements in Radiance Fields have significantly improved novel-view synthesis. However, in many real-world applications, the more advanced challenge lies in inverse rendering, which seeks to derive the physical properties of a…
Materials designed by nature commonly exhibit functional grading and laminated structures, particularly when intended for enhanced impact protection. Synthetic materials have also found success in exploiting this concept with fully dense…
Materials science datasets are inherently heterogeneous and are available in different modalities such as characterization spectra, atomic structures, microscopic images, and text-based synthesis conditions. The advancements in multi-modal…
Shape matching has been a long-studied problem for the computer graphics and vision community. The objective is to predict a dense correspondence between meshes that have a certain degree of deformation. Existing methods either consider the…
To leverage advancements in machine learning for metallic materials design and property prediction, it is crucial to develop a data-reduced representation of metal microstructures that surpasses the limitations of current physics-based…
Designing heterogeneous, self-assembling systems is a central challenge in soft matter and biology. We present a framework that uses gradient-based optimization to invert an analytical yield calculation, tuning systems toward target…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
Understanding structure-property relationships in complex materials requires integrating complementary measurements across multiple length scales. Here we propose an interpretable "multimodal" machine learning framework that unifies…
In this paper we develop automatic shape differentiation techniques for unfitted discretisations and link these to recent advances in shape calculus for unfitted methods. We extend existing analytic shape calculus results to the case where…
This paper proposes a variational framework for multi-objective level set topology optimization. The approach interprets the level set function as a generalized coordinate of a fictitious material and derives its equation of motion from…
In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between the layers, while close packing of the layers…
Implicit neural representations map a shape-specific latent code and a 3D coordinate to its corresponding signed distance (SDF) value. However, this approach only offers a single level of detail. Emulating low levels of detail can be…
We present a computational design methodology for topology optimization of multi-material-based flexoelectric composites. The methodology extends our recently proposed design methodology for a single flexoelectric material. We adopt the…