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We propose a multiscale method for mixed-dimensional elliptic problems with highly heterogeneous coefficients arising, for example, in the modeling of fractured porous media. The method is based on the Localized Orthogonal Decomposition…
Efficient and high-fidelity polarization demosaicking is critical for industrial applications of the division of focal plane (DoFP) polarization imaging systems. However, existing methods have an unsatisfactory balance of speed, accuracy,…
The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on…
3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces or non-manifold parts, which pose problems in obtaining a 3D…
We present an efficient, trivially parallelizable algorithm to compute offset surfaces of shapes discretized using a dexel data structure. Our algorithm is based on a two-stage sweeping procedure that is simple to implement and efficient,…
A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The construction begins with a harmonic approximation of the…
This paper derives a posteriori error estimates for the mixed numerical approximation of the Laplace eigenvalue problem with homogeneous Dirichlet boundary conditions. In particular, the resulting error estimator constitutes an upper bound…
Recently, a nonconforming surface finite element was developed to discretize 3d vector-valued compressible flow problems arising in climate modeling. In this contribution we derive an error analysis for this approach on a vector-valued…
Intrinsic decomposition is a fundamental mid-level vision problem that plays a crucial role in various inverse rendering and computational photography pipelines. Generating highly accurate intrinsic decompositions is an inherently…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an…
The direct method is one of the most important algorithms for solving linear systems of equations, with LU decomposition comprising a significant portion of its computation time. This study explores strategies to accelerate complex LU…
It is well known that multiplication operations in convolutional layers of common CNNs consume a lot of time during inference stage. In this article we present a flexible method to decrease both computational complexity of convolutional…
Implicit curve and surface reconstruction attracts the attention of many researchers and gains a wide range of applications, due to its ability to describe objects with complicated geometry and topology. However, extra zero-level sets or…
The hierarchical interpolative factorization for elliptic partial differential equations is a fast algorithm for approximate sparse matrix inversion in linear or quasilinear time. Its accuracy can degrade, however, when applied to strongly…
In the process of projecting the surface of a three-dimensional object onto a two-dimensional surface, due to the perspective distortion, the image on the surface of the object will have different degrees of distortion according to the…
We consider a diffuse interface approach for solving an elliptic PDE on a given closed hypersurface. The method is based on a (bulk) finite element scheme employing numerical quadrature for the phase field function and hence is very easy to…
Using a deterministic framework allows us to estimate a function with the purpose of interpolating data in spatial statistics. Radial basis functions are commonly used for scattered data interpolation in a d-dimensional space, however,…
This work develops optimal preconditioners for the discrete H(curl) and H(div) problems on two-dimensional surfaces by nodal auxiliary space preconditioning [R. Hiptmair, J. Xu: SIAM J. Numer. Anal. \textbf{45}, 2483-2509 (2007)]. In…
For some kernel matrices, low-rank approximations can be quickly obtained via analytic techniques. One important class of analytic methods that has received attention in recent years is based on the use of proxy points. Accuracy analysis…