Propagating Geometry Information to Finite Element Computations

The traditional workflow in continuum mechanics simulations is that a geometry description —for example obtained using Constructive Solid Geometry (CSG) or Computer Aided Design (CAD) tools—forms the input for a mesh generator. The mesh is then used as the sole input for the finite element, finite volume, and finite difference solver, which at this point no longer has access to the original, “underlying” geometry. However, many modern techniques—for example, adaptive mesh refinement and the use of higher order geometry approximation methods—really do need information about the underlying geometry to realize their full potential. We have undertaken an exhaustive study of where typical finite element codes use geometry information, with the goal of determining what information geometry tools would have to provide. Our study shows that nearly all geometry-related needs inside the simulators can be satisfied by just two “primitives”: elementary queries posed by the simulation software to the geometry description. We then show that it is possible to provide these primitives in all of the frequently used ways in which geometries are described in common industrial workflows, and illustrate our solutions using a number of examples.

A New Numerical Nuclear Reactor Neutronics Code SHARK

In order to establish the next-generation reactor physics calculation method based on the numerical nuclear reactor technology and realize high-fidelity modeling and calculation, a new numerical nuclear reactor neutronics code SHARK is developed. The code is based on the direct transport method with construct solid geometry (CSG) method, advanced subgroup resonance method, direct transport MOC method in rectangle and hexagonal geometry, large-scale parallel, and CMFD acceleration method. The C5G7, macro BEAVRS and VERA benchmarks are verified to show the accuracy of the code and method. Numerical results show good accuracy and calculation performance of SHARK, and the direct transport method can be adopted on numerical nuclear reactor calculation.

Raymarching Distance Fields with CUDA

Raymarching is a technique for rendering implicit surfaces using signed distance fields. It has been known and used since the 1980s for rendering fractals and CSG (constructive solid geometry) surfaces, but has rarely been used for commercial rendering applications such as film and 3D games. Raymarching was first used for photorealistic rendering in the mid 2000s by demoscene developers and hobbyist graphics programmers, receiving little to no attention from the academic community and professional graphics engineers. In the present work, we explain why the use of Simple and Fast Multimedia Library (SFML) by nearly all existing approaches leads to a number of inefficiencies, and hence set out to develop a CUDA oriented approach instead. We next show that the usual data handling pipeline leads to further unnecessary data flow overheads and therefore propose a novel pipeline structure that eliminates much of redundancy in the manner in which data are processed and passed. We proceed to introduce a series of data structures which were designed with the specific aim of exploiting the pipeline’s strengths in terms of efficiency while achieving a high degree of photorealism, as well as the accompanying models and optimizations that ultimately result in an engine which is capable of photorealistic and real-time rendering on complex scenes and arbitrary objects. Lastly, the effectiveness of our framework is demonstrated in a series of experiments which compare our engine both in terms of visual fidelity and computational efficiency with the leading commercial and open source solutions, namely Unreal Engine and Blender.

PROBLEM POSING DAN STRATEGI METAKOGNISI PESERTA DIDIK DALAM MATERI BANGUN RUANG DI SMK

ABSTRAKProblem posing dan strategi metakognisi merupakan keterampilan berpikir tingkat tinggi dan sangat penting dikuasai oleh peserta didik. Penelitian ini bertujuan untuk mendeskripsikan kemampuan problem posing, strategi metakognisi peserta didik, hubungan kemampuan problem posing dan strategi metakognisi peserta didik. Penelitian ini menggunakan metode kombinasi sequential exploratory. Sumber data penelitian ini adalah peserta didik kelas XI Multimedia. Data berupa hasil tes uraian dan hasil wawancara semi-terstruktur. Tes uraian terdiri sebanyak tiga soal yang meminta peserta didik untuk mengajukan masalah berdasarkan indikator situasi problem posing yang telah ditetapkan pada soal. Peserta didik diminta untuk mengajukan masalah matematis bangun ruang sisi lengkung pada situasi bebas, situasi semi-terstruktur, dan situasi terstruktur. Menyelesaikan masalah matematis bangun ruang sisi lengkung mengggunakan strategi metakognisi. Setelah itu akan dilakukan wawancara semi-terstruktur terhadap tiga peserta didik untuk memperdalam data dan mengungkap lebih lanjut mengenai kemampuan problem posing dan strategi metakognisi yang tidak terlihat pada hasil tes uraian. Kemampuan peserta didik dalam mengajukan masalah lebih dominan pada situasi bebas dan semi-terstruktur. Strategi metakognisi secara signifikan mempengaruhi kinerja aktual keterampilan pengajuan masalah dan penyelesaian masalah matematis. Hasil penelitian juga menunjukkan hubungan kemampuan problem posing dan strategi metakognisi dengan Pearson Correlation sebesar 0,72 yang berarti merupakan korelasi kuat dan memiliki hubungan yang positif.Kata Kunci: Problem Posing, Strategi Metakognisi, Bangun Ruang Sisi LengkungABSTRACTProblem-posing and metacognition strategies are high-level thinking skills and are very important to be mastered by students. This study aims to describe problem-posing abilities, students' metacognition strategies, the relationship between problem-posing abilities and students' metacognition strategies. This study uses a sequential exploratory combination method. The data sources of this research are students of class XI Multimedia. The data are in the form of description test results and semi-structured interview results. The description test consists of three questions that ask students to pose problems based on the problem-posing situation indicators set on the questions. Students are asked to pose a mathematical problem of solid geometry in free situations, semi-structured situations, and structured situations. They are solving mathematical problems of solid geometry using metacognition strategies. After that, interviews with three students will be conducted to deepen the data and reveal more about problem-posing abilities and metacognition strategies that are not seen in the results of the description test. The ability of students to pose problems is more dominant in free and semi-structured situations. Metacognition strategies significantly affect the actual performance of problem-posing and mathematical problem-solving skills. The results also show the relationship between problem-posing abilities and metacognition strategies with the Pearson Correlation of 0.72, which means it is a strong correlation and has a positive relationship.Keywords: Problem Posing, Metacognition Strategy, Solid Geometry

Coda

These interesting situations in which generics play a key role in interactional pragmatics sparked my memory of solid geometry and spherical trigonometry class at Stuyvesant High School in the early 1960s. Each morning our instructor, the somewhat irascible Mr. Burns, would start off by asking a question on the day's material, calling for a response by ‘[student surname]’. Stuyvesant, in those days an all-male institution, functioned, like prep schools, on a surname basis for both reference and address; the teachers’ names were prefaced by Mr. or Mrs. or Miss, while student names had no prefixed title.

Influence of 3D-Printed TPU Properties for the Design of Elastic Products

The design of products with elastic properties is a paradigm for design engineers because the properties of the material define the correct functionality of the product. Fused filament fabrication (FFF) allows for the printing of products in thermoplastic polyurethanes (TPU). Therefore, it offers the ability to design elastic products with the freedom of forms that this technology allows and also with greater variation of elastic properties than with a conventional process. The internal structures and the variation in thickness that can be used facilitate the design of products with different elastic realities, producing variations in the elasticity of the product with the same material. This work studies the influence of the variation of internal density as a function of basic geometries in order to quantify the difference in elasticity produced on a product when it is designed. Likewise, a case study was carried out with the creation of a fully elastic computer keyboard printed in 3D. The specimens were subjected to compression to characterize the behavior of the structures. The tests showed that the elasticity varies depending on the orientation and geometry, with the highest compressive strength observed in the vertical orientation with 80% lightening. In addition, the internal lightening increases the elasticity progressively but not uniformly with respect to the solid geometry, and also the flat faces favour the reduction in elasticity. This study classifies the behavior of TPU with the aim of being applied to the design and manufacture of products with specific properties. In this work, a totally flexible and functional keyboard was designed, obtaining elasticity values that validate the study carried out.

ETNOMATEMATIKA: KEKAYAAN BUDAYA KABUPATEN ALOR SEBAGAI SUMBER MEDIA PEMBELAJARAN MATEMATIKA DI SEKOLAH DASAR

Ethnomatematics presents as a bridge between culture and mathematics. Awareness of the importance of preserving culture early on and presenting the context of real situations in the mathematical learning process is the basis of this research. Ethnomatematika sourced from the local culture of Alor Regency is very rich and can be used as a media of mathematics learning but has not been explored in depth. The purpose of this study is to associate ethnomatematics of Alor Regency with the context of learning in elementary schools. This research is qualitative with an explorative, descriptive, and ethnography approach. Data retrieval techniques using interviews, observations, and documentation. Data collection was carried out in January to February 2021. The results of the study found elements of ethnomatematics derived from traditional clothing and accessories, dowry, traditional clothing, earthenware, war tools, musical instruments, fishing instruments, traditional houses, and traditional games. Ethnomatematics product can be used on the basic competencies of plane geometry, solid geometry, symmetry, mirroring, symmetry, arithmetic, interline relationships, angular types, inter-angle relationships, and measurements in elementary schools. Abstrak Etnomatematika hadir sebagai sarana untuk menjembatani antara budaya dan matematika. Kesadaran akan pentingnya melestarikan budaya sejak dini dan menghadirkan konteks situasi nyata dalam proses pembelajaran matematika merupakan landasan dilakukannya penelitian ini. Etnomatematika yang bersumber dari budaya lokal Kabupaten Alor sangat kaya dan dapat digunakan sebagai media pembelajaran matematika namun selama ini tidak dieksplorasi secara mendalam. Tujuan dari penelitian ini adalah untuk mengaitkan etnomatematika Kabupaten Alor dengan konteks pembelajaran di sekolah dasar. Penelitian merupakan kualitatif dengan pendekatan eksploratif, deskriptif, dan etnografi. Teknik pengambilan data menggunakan wawancara, observasi, dan dokumentasi. Pengumpulan data dilakukan pada bulan Januari hingga Februari 2021. Hasil penelitian menemukan unsur etnomatematika yang berasal dari pakaian adat beserta asesorisnya, mas kawin, pakaian adat, gerabah, alat perang, alat musik, alat menangkap ikan, rumah adat, serta permainan masyarakat lokal. Produk etnomatematika ini dapat digunakan sebagai media pembelajaran pada kompetensi dasar bangun datar, bangun ruang, kesimetrisan, pencerminan, aritmatika, hubungan antar garis, jenis-jenis sudut, hubungan antar sudut, dan pengukuran di sekolah dasar. Kata Kunci: Etnomatematika, Media Pembelajaran Matematika, Sekolah Dasar