The geometric construction of finite element spaces suitable for complicated shapes or microstructured materials is discussed. As an application, the efficient computation of linearized elasticity is considered on them. Geometries are supposed to be implicitly described via 3D voxel data (e. g. μCT scans) associated with a cubic grid. We place degrees of freedom only at the grid nodes and incor...

We present a novel algorithm to compute cache-efficient layouts of bounding volume hierarchies (BVHs) of polygonal models. Our approach does not make any assumptions about the cache parameters or block sizes of the memory hierarchy. We introduce a new probabilistic model to predict the runtime access patterns of a BVH. Our layout computation algorithm utilizes parent-child and spatial localitie...

Some direct relations between soliton solutions of integrable hierarchies and thermodynamical quantities of the Coulomb plasmas on the plane are revealed. We find that certain soliton solutions of the Kadomtsev-Petviashvili (KP) and B-type KP (BKP) hierarchies describe two-dimensional one or two component plasmas at special boundary conditions and fixed temperatures. It is shown that different ...

Traditional urban planning demands experts to spend much time producing an optimal plan under many architectural constraints. The remarkable imaginative ability of deep generative learning provides hope for renovating this domain. Existing works are constrained by: (1) neglecting human requirements; (2) omitting spatial hierarchies, and (3) lacking samples. We propose a novel, human-instructed ...