Mathematical Software
We present a new variant of serial right-looking supernodal sparse Cholesky factorization (RL). Our comparison of RL with the multifrontal method confirms that RL is simpler, slightly faster, and requires slightly less storage. The key to…
We address the parallelization of the LU factorization of hierarchical matrices ($\mathcal{H}$-matrices) arising from boundary element methods. Our approach exploits task-parallelism via the OmpSs programming model and runtime, which…
Uncertainty Quantification (UQ) is vital to safety-critical model-based analyses, but the widespread adoption of sophisticated UQ methods is limited by technical complexity. In this paper, we introduce UM-Bridge (the UQ and Modeling…
The Prony method for approximating signals comprising sinusoidal/exponential components is known through the pioneering work of Prony in his seminal dissertation in the year 1795. However, the Prony method saw the light of real world…
Data assimilation techniques are often confronted with challenges handling complex high dimensional physical systems, because high precision simulation in complex high dimensional physical systems is computationally expensive and the exact…
PySLSQP is a seamless interface for using the SLSQP algorithm from Python. It wraps the original SLSQP Fortran code sourced from the SciPy repository and provides a host of new features to improve the research utility of the original…
In this paper, a run-time auto-tuning method for performance parameters according to input matrices is proposed. RAO-SS (Run-time Auto-tuning Optimizer for Sparse Solvers), which is a prototype of auto-tuning software using the proposed…
The implementation process of a $\texttt{RestrictedFunctionSpace}$ class in Firedrake, a Python library which numerically solves partial differential equations through the use of the finite element method, is documented. This includes an…
OpenLB is an object-oriented implementation of LBM. It is the first implementation of a generic platform for LBM programming, which is shared with the open source community (GPLv2). Since the first release in 2007, the code has been…
Fast and accurate numerical simulations are crucial for designing large-scale geological carbon storage projects ensuring safe long-term CO2 containment as a climate change mitigation strategy. These simulations involve solving numerous…
Differentiable numerical simulations of physical systems have gained rising attention in the past few years with the development of automatic differentiation tools. This paper presents JAX-SSO, a differentiable finite element analysis…
In this study, we introduce HOBOTAN, a new solver designed for Higher Order Binary Optimization (HOBO). HOBOTAN supports both CPU and GPU, with the GPU version developed based on PyTorch, offering a fast and scalable system. This solver…
Mittag-Leffler correlated noise (M-L noise) plays a crucial role in the dynamics of complex systems, yet the scientific community has lacked tools for its direct generation. Addressing this gap, our work introduces GenML, a Python library…
$k$-diagonal circulant matrices and cyclic banded matrices are widely used in numerical simulations and signal processing of circular linear systems. Algorithms that directly involve or specify linear or quadratic complexity for the…
In this paper, we explore the acceleration of tensor product operations in finite element methods, leveraging the computational power of the NVIDIA A100 GPU Tensor Cores. We provide an accessible overview of the necessary mathematical…
This contribution examines the capabilities of the Python ecosystem to solve nonlinear energy minimization problems, with a particular focus on transitioning from traditional MATLAB methods to Python's advanced computational tools, such as…
We present ATC, a C++ library for advanced Tucker-based lossy compression of dense multidimensional numerical data in a shared-memory parallel setting, based on the sequentially truncated higher-order singular value decomposition (ST-HOSVD)…
Many problems in Physics and Chemistry are formulated as the minimization of a functional. Therefore, methods for solving these problems typically require differentiating maps whose input and/or output are functions -- commonly referred to…
OpenCAEPoro is a parallel numerical simulation software developed in C++ for simulating multiphase and multicomponent flows in porous media. The software utilizes a set of general-purpose compositional model equations, enabling it to handle…
Component-Based Software Engineering (CBSE) is a methodology that assembles pre-existing, re-usable software components into new applications, which is particularly relevant for fast moving, data-intensive fields such as bioinformatics.…