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The image reconstruction of chromophore concentrations using Diffuse Optical Tomography (DOT) data can be described mathematically as an ill-posed inverse problem. Recent work has shown that the use of hyperspectral DOT data, as opposed to…
A spectral element method (SEM) is developed to solve polarized radiative transfer in multidimensional participating medium. The angular discretization is based on the discrete-ordinates approach, and the spatial discretization is conducted…
In this paper, we present a dimension reduction method to reduce the dimension of parameter space and state space and efficiently solve inverse problems. To this end, proper orthogonal decomposition (POD) and radial basis function (RBF) are…
We address the problem of recovering the shape and spatially-varying reflectance of an object from multi-view images (and their camera poses) of an object illuminated by one unknown lighting condition. This enables the rendering of novel…
The numerical analysis of stochastic time fractional evolution equations presents considerable challenges due to the limited regularity of the model caused by the nonlocal operator and the presence of noise. The existing time-stepping…
Meshfree radial basis function (RBF) methods are popular tools used to numerically solve partial differential equations (PDEs). They take advantage of being flexible with respect to geometry, easy to implement in higher dimensions, and can…
Neural Radiance Field (NeRF) is a popular method in representing 3D scenes by optimising a continuous volumetric scene function. Its large success which lies in applying volumetric rendering (VR) is also its Achilles' heel in producing…
Reconstructing the shape and appearance of real-world objects using measured 2D images has been a long-standing problem in computer vision. In this paper, we introduce a new analysis-by-synthesis technique capable of producing high-quality…
The expedient design of precision components in aerospace and other high-tech industries requires simulations of physical phenomena often described by partial differential equations (PDEs) without exact solutions. Modern design problems…
The increasing complexity and scale of photonic and electromagnetic devices demand efficient and accurate numerical solvers. In this work, we develop a parallel overlapping domain decomposition method (DDM) based on the finite-difference…
The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple…
Neural radiance fields (NeRF) have gained prominence as a machine learning technique for representing 3D scenes and estimating the bidirectional reflectance distribution function (BRDF) from multiple images. However, most existing research…
General purpose optimization techniques can be used to solve many problems in engineering computations, although their cost is often prohibitive when the number of degrees of freedom is very large. We describe a multilevel approach to speed…
The Intrinsic Surface Finite Element Method (ISFEM) was recently proposed to solve Partial Differential Equations (PDEs) on surfaces. ISFEM proceeds by writing the PDE with respect to a local coordinate system anchored to the surface and…
We present a scheme for fast environment light estimation from the RGBD appearance of individual objects and their local image areas. Conventional inverse rendering is too computationally demanding for real-time applications, and the…
Penetration depth calculation quantifies the extent of overlap between two objects and is crucial in fields like simulations, the metaverse, and robotics. Recognizing its significance, efforts have been made to accelerate this computation…
New web technologies have enabled the deployment of powerful GPU-based computational pipelines that run entirely in the web browser, opening a new frontier for accessible scientific visualization applications. However, these new…
Rotation measure (RM) synthesis is a widely used polarization processing algorithm for reconstructing polarized structures along the line of sight. Performing RM synthesis on large datasets produced by telescopes like LOFAR can be…
The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point representation…
Multigrid solvers are the standard in modern scientific computing simulations. Domain Decomposition Aggregation-Based Algebraic Multigrid, also known as the DD-$\alpha$AMG solver, is a successful realization of an algebraic multigrid solver…