11,525 research outputs found
Fast matrix multiplication techniques based on the Adleman-Lipton model
On distributed memory electronic computers, the implementation and
association of fast parallel matrix multiplication algorithms has yielded
astounding results and insights. In this discourse, we use the tools of
molecular biology to demonstrate the theoretical encoding of Strassen's fast
matrix multiplication algorithm with DNA based on an -moduli set in the
residue number system, thereby demonstrating the viability of computational
mathematics with DNA. As a result, a general scalable implementation of this
model in the DNA computing paradigm is presented and can be generalized to the
application of \emph{all} fast matrix multiplication algorithms on a DNA
computer. We also discuss the practical capabilities and issues of this
scalable implementation. Fast methods of matrix computations with DNA are
important because they also allow for the efficient implementation of other
algorithms (i.e. inversion, computing determinants, and graph theory) with DNA.Comment: To appear in the International Journal of Computer Engineering
Research. Minor changes made to make the preprint as similar as possible to
the published versio
AlSub: Fully Parallel and Modular Subdivision
In recent years, mesh subdivision---the process of forging smooth free-form
surfaces from coarse polygonal meshes---has become an indispensable production
instrument. Although subdivision performance is crucial during simulation,
animation and rendering, state-of-the-art approaches still rely on serial
implementations for complex parts of the subdivision process. Therefore, they
often fail to harness the power of modern parallel devices, like the graphics
processing unit (GPU), for large parts of the algorithm and must resort to
time-consuming serial preprocessing. In this paper, we show that a complete
parallelization of the subdivision process for modern architectures is
possible. Building on sparse matrix linear algebra, we show how to structure
the complete subdivision process into a sequence of algebra operations. By
restructuring and grouping these operations, we adapt the process for different
use cases, such as regular subdivision of dynamic meshes, uniform subdivision
for immutable topology, and feature-adaptive subdivision for efficient
rendering of animated models. As the same machinery is used for all use cases,
identical subdivision results are achieved in all parts of the production
pipeline. As a second contribution, we show how these linear algebra
formulations can effectively be translated into efficient GPU kernels. Applying
our strategies to , Loop and Catmull-Clark subdivision shows
significant speedups of our approach compared to state-of-the-art solutions,
while we completely avoid serial preprocessing.Comment: Changed structure Added content Improved description
Accurate and efficient algorithms for boundary element methods in electromagnetic scattering: a tribute to the work of F. Olyslager
Boundary element methods (BEMs) are an increasingly popular approach to model electromagnetic scattering both by perfect conductors and dielectric objects. Several mathematical, numerical, and computational techniques pullulated from the research into BEMs, enhancing its efficiency and applicability. In designing a viable implementation of the BEM, both theoretical and practical aspects need to be taken into account. Theoretical aspects include the choice of an integral equation for the sought after current densities on the geometry's boundaries and the choice of a discretization strategy (i.e. a finite element space) for this equation. Practical aspects include efficient algorithms to execute the multiplication of the system matrix by a test vector (such as a fast multipole method) and the parallelization of this multiplication algorithm that allows the distribution of the computation and communication requirements between multiple computational nodes. In honor of our former colleague and mentor, F. Olyslager, an overview of the BEMs for large and complex EM problems developed within the Electromagnetics Group at Ghent University is presented. Recent results that ramified from F. Olyslager's scientific endeavors are included in the survey
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