index.json

[{"authors":null,"categories":null,"content":"I am a researcher at the Institute of Applied Geometry of Johannes Kepler University Linz. My research interests are at the crossroads of geometric modeling, numerical analysis and geometric deep learning.\n","date":-62135596800,"expirydate":-62135596800,"kind":"term","lang":"en","lastmod":-62135596800,"objectID":"2525497d367e79493fd32b198b28f040","permalink":"","publishdate":"0001-01-01T00:00:00Z","relpermalink":"","section":"authors","summary":"I am a researcher at the Institute of Applied Geometry of Johannes Kepler University Linz. My research interests are at the crossroads of geometric modeling, numerical analysis and geometric deep learning.","tags":null,"title":"Dr. Felix Scholz","type":"authors"},{"authors":[],"categories":null,"content":" Click on the Slides button above to view the built-in slides feature. Slides can be added in a few ways:\nCreate slides using Wowchemy’s Slides feature and link using slides parameter in the front matter of the talk file Upload an existing slide deck to static/ and link using url_slides parameter in the front matter of the talk file Embed your slides (e.g. Google Slides) or presentation video on this page using shortcodes. Further event details, including page elements such as image galleries, can be added to the body of this page.\n","date":1906549200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1906549200,"objectID":"a8edef490afe42206247b6ac05657af0","permalink":"https://felixfeliz.github.io/talk/high-order-numerical-integration-for-trimmed-isogeometric-analysis/","publishdate":"2017-01-01T00:00:00Z","relpermalink":"/talk/high-order-numerical-integration-for-trimmed-isogeometric-analysis/","section":"event","summary":"An example talk using Wowchemy's Markdown slides feature.","tags":[],"title":"High-order numerical integration for trimmed Isogeometric Analysis","type":"event"},{"authors":["Felix Scholz","Soma Nishikawa","Masahito Takezawa","Takashi Maekawa"],"categories":null,"content":"","date":1640995200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1640995200,"objectID":"716765adcdb8d988eafc0eb019390ce2","permalink":"https://felixfeliz.github.io/publication/a-99-developable/","publishdate":"2023-02-18T18:38:09.813098Z","relpermalink":"/publication/a-99-developable/","section":"publication","summary":"","tags":null,"title":"Approximation of doubly curved surfaces by analysis-suitable piecewise surfaces with high developability","type":"publication"},{"authors":["Maodong Pan","Bert Jüttler","Felix Scholz"],"categories":null,"content":"","date":1640995200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1640995200,"objectID":"91bb0a50fca71f57c37e07d0b768f3c6","permalink":"https://felixfeliz.github.io/publication/a-80-hierarchical/","publishdate":"2023-02-18T18:38:09.81482Z","relpermalink":"/publication/a-80-hierarchical/","section":"publication","summary":"Hierarchical B-splines, which possess the local refinement capability, have been recognized as a useful tool in the context of isogeometric analysis. However, similar as for tensor-product B-splines, isogeometric simulations with hierarchical B-splines face a big computational burden from the perspective of matrix assembly, particularly if the spline degree p is high. To address this issue, we extend the recent work (Pan et al., 2020) – which introduced an efficient assembling approach for tensor-product B-splines – to the case of hierarchical B-splines. In the new approach, the integrand factor is transformed into piecewise polynomials via quasi-interpolation. Subsequently, the resulting elementary integrals are pre-computed and stored in a look-up table. Finally, the sum-factorization technique is adopted to accelerate the assembly process. We present a detailed analysis, which reveals that the presented method achieves the expected complexity of O(pd+1) per degree of freedom (without taking sparse matrix operations into account) under the assumption of mesh admissibility. We verify the efficiency of the new method by applying it to an elliptic problem on the three-dimensional domain and a parabolic problem on the four-dimensional domain in space–time, respectively. A comparison with standard Gaussian quadrature is also provided.","tags":["Isogeometric analysis","Hierarchical B-splines","Assembling matrices","Spline projection","Looking up and sum-factorization","Complexity"],"title":"Efficient matrix computation for isogeometric discretizations with hierarchical B-splines in any dimension","type":"publication"},{"authors":["Chiu Ling Chan","Felix Scholz","Thomas Takacs"],"categories":null,"content":"","date":1640995200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1640995200,"objectID":"2639eb4883c6ec0e2075257b7a2d0dff","permalink":"https://felixfeliz.github.io/publication/a-90-lit/","publishdate":"2023-02-18T18:38:09.814094Z","relpermalink":"/publication/a-90-lit/","section":"publication","summary":"","tags":null,"title":"Locally refined quad meshing for linear elasticity problems based on convolutional neural networks","type":"publication"},{"authors":["Felix Scholz","Takashi Maekawa"],"categories":null,"content":"","date":1609459200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1609459200,"objectID":"6868f7b12c41da3b3006914f4623e6e4","permalink":"https://felixfeliz.github.io/publication/a-70-geodesic/","publishdate":"2023-02-18T18:38:09.816262Z","relpermalink":"/publication/a-70-geodesic/","section":"publication","summary":"","tags":null,"title":"Accurate High-Order Derivatives of Geodesic Paths on Smooth Surfaces","type":"publication"},{"authors":["Takashi Maekawa","Felix Scholz"],"categories":null,"content":"","date":1609459200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1609459200,"objectID":"860022215353ee53f56952bb86da9f9b","permalink":"https://felixfeliz.github.io/publication/a-75-geodesicjp/","publishdate":"2023-02-18T18:38:09.815583Z","relpermalink":"/publication/a-75-geodesicjp/","section":"publication","summary":"","tags":null,"title":"Accurate higher order derivatives of curvature and torsion of geodesic curves on freeform surfaces (Application to geodesic grid models)","type":"publication"},{"authors":["Felix Scholz","Bert Jüttler"],"categories":null,"content":"","date":1609459200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1609459200,"objectID":"f10ef94a76e0c5f82e3274043858a07b","permalink":"https://felixfeliz.github.io/publication/a-50-scholz-2021101977/","publishdate":"2023-02-18T18:38:09.823892Z","relpermalink":"/publication/a-50-scholz-2021101977/","section":"publication","summary":"Finding the optimal parameterization for fitting a given sequence of data points with a parametric curve is a challenging problem that is equivalent to solving a highly non-linear system of equations. In this work, we propose the use of a residual neural network to approximate the function that assigns to a sequence of data points a suitable parameterization for fitting a polynomial curve of a fixed degree. Our model takes as an input a small fixed number of data points and the generalization to arbitrary data sequences is obtained by performing multiple evaluations. We show that the approach compares favorably to classical methods in a number of numerical experiments that include the parameterization of polynomial as well as non-polynomial data.","tags":["Parameterization","Curve fitting","Deep learning"],"title":"Parameterization for polynomial curve approximation via residual deep neural networks","type":"publication"},{"authors":["Felix Scholz","Bert Jüttler"],"categories":null,"content":"","date":1609459200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1609459200,"objectID":"8520df65ed4ac4775bb3fe9419cfcdc0","permalink":"https://felixfeliz.github.io/publication/a-60-scholz-2021-using/","publishdate":"2023-02-18T18:38:09.821706Z","relpermalink":"/publication/a-60-scholz-2021-using/","section":"publication","summary":"","tags":null,"title":"Using High-Order Transport Theorems for Implicitly Defined Moving Curves to Perform Quadrature on Planar Domains","type":"publication"},{"authors":[],"categories":[],"content":"Create slides in Markdown with Wowchemy Wowchemy | Documentation\nFeatures Efficiently write slides in Markdown 3-in-1: Create, Present, and Publish your slides Supports speaker notes Mobile friendly slides Controls Next: Right Arrow or Space Previous: Left Arrow Start: Home Finish: End Overview: Esc Speaker notes: S Fullscreen: F Zoom: Alt + Click PDF Export Code Highlighting Inline code: variable\nCode block:\nporridge = \u0026#34;blueberry\u0026#34; if porridge == \u0026#34;blueberry\u0026#34;: print(\u0026#34;Eating...\u0026#34;) Math In-line math: $x + y = z$\nBlock math:\n$$ f\\left( x \\right) = ;\\frac{{2\\left( {x + 4} \\right)\\left( {x - 4} \\right)}}{{\\left( {x + 4} \\right)\\left( {x + 1} \\right)}} $$\nFragments Make content appear incrementally\n{{% fragment %}} One {{% /fragment %}} {{% fragment %}} **Two** {{% /fragment %}} {{% fragment %}} Three {{% /fragment %}} Press Space to play!\nOne Two Three A fragment can accept two optional parameters:\nclass: use a custom style (requires definition in custom CSS) weight: sets the order in which a fragment appears Speaker Notes Add speaker notes to your presentation\n{{% speaker_note %}} - Only the speaker can read these notes - Press `S` key to view {{% /speaker_note %}} Press the S key to view the speaker notes!\nOnly the speaker can read these notes Press S key to view Themes black: Black background, white text, blue links (default) white: White background, black text, blue links league: Gray background, white text, blue links beige: Beige background, dark text, brown links sky: Blue background, thin dark text, blue links night: Black background, thick white text, orange links serif: Cappuccino background, gray text, brown links simple: White background, black text, blue links solarized: Cream-colored background, dark green text, blue links Custom Slide Customize the slide style and background\n{{\u0026lt; slide background-image=\u0026#34;/media/boards.jpg\u0026#34; \u0026gt;}} {{\u0026lt; slide background-color=\u0026#34;#0000FF\u0026#34; \u0026gt;}} {{\u0026lt; slide class=\u0026#34;my-style\u0026#34; \u0026gt;}} Custom CSS Example Let’s make headers navy colored.\nCreate assets/css/reveal_custom.css with:\n.reveal section h1, .reveal section h2, .reveal section h3 { color: navy; } Questions? Ask\nDocumentation\n","date":1549324800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1549324800,"objectID":"0e6de1a61aa83269ff13324f3167c1a9","permalink":"https://felixfeliz.github.io/slides/example/","publishdate":"2019-02-05T00:00:00Z","relpermalink":"/slides/example/","section":"slides","summary":"An introduction to using Wowchemy's Slides feature.","tags":[],"title":"Slides","type":"slides"},{"authors":["Felix Scholz","Angelos Mantzaflaris","Bert Jüttler"],"categories":null,"content":"","date":1546300800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1546300800,"objectID":"7b1dccaa743d4581b7586ade66f22436","permalink":"https://felixfeliz.github.io/publication/a-302-d-paper/","publishdate":"2023-02-18T18:38:09.827394Z","relpermalink":"/publication/a-302-d-paper/","section":"publication","summary":"","tags":null,"title":"First order error correction for trimmed quadrature in isogeometric analysis","type":"publication"},{"authors":["Angelos Mantzaflaris","Felix Scholz","Ioannis Toulopoulos"],"categories":null,"content":"","date":1546300800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1546300800,"objectID":"f5599aeac5bdbd40d59955cb08d29b48","permalink":"https://felixfeliz.github.io/publication/a-20-smt-17/","publishdate":"2023-02-18T18:38:09.828987Z","relpermalink":"/publication/a-20-smt-17/","section":"publication","summary":"","tags":null,"title":"Low-rank space-time decoupled isogeometric analysis for parabolic problems with varying coefficients","type":"publication"},{"authors":["Felix Scholz","Bert Jüttler"],"categories":null,"content":"","date":1546300800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1546300800,"objectID":"3b046d743947a95d48db4bb78bae5536","permalink":"https://felixfeliz.github.io/publication/a-40-scholz-2019112577/","publishdate":"2023-02-18T18:38:09.825654Z","relpermalink":"/publication/a-40-scholz-2019112577/","section":"publication","summary":"We present a novel technique for the numerical integration of trivariate functions on trimmed domains. In our setting, we assume that the trimming surface is defined implicitly. Our approach combines a linear approximation of the trimming surface with a correction term. The latter term makes it possible to achieve a cubic convergence rate, which is one order higher than the rate obtained by using the linear approximation only. We also present numerical experiments that demonstrate the method’s potential for applications in isogeometric analysis.","tags":["Trimming","Isogeometric analysis","Numerical integration","Quadrature"],"title":"Numerical integration on trimmed three-dimensional domains with implicitly defined trimming surfaces","type":"publication"},{"authors":["Felix Scholz","Angelos Mantzaflaris","Bert Jüttler"],"categories":null,"content":"","date":1514764800,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1514764800,"objectID":"5ebfee357be2ae25265d93f33d6de71e","permalink":"https://felixfeliz.github.io/publication/a-10-scholz-2018485/","publishdate":"2023-02-18T18:38:09.830283Z","relpermalink":"/publication/a-10-scholz-2018485/","section":"publication","summary":"","tags":null,"title":"Partial tensor decomposition for decoupling isogeometric Galerkin discretizations","type":"publication"},{"authors":null,"categories":null,"content":"Lorem ipsum dolor sit amet, consectetur adipiscing elit. Duis posuere tellus ac convallis placerat. Proin tincidunt magna sed ex sollicitudin condimentum. Sed ac faucibus dolor, scelerisque sollicitudin nisi. Cras purus urna, suscipit quis sapien eu, pulvinar tempor diam. Quisque risus orci, mollis id ante sit amet, gravida egestas nisl. Sed ac tempus magna. Proin in dui enim. Donec condimentum, sem id dapibus fringilla, tellus enim condimentum arcu, nec volutpat est felis vel metus. Vestibulum sit amet erat at nulla eleifend gravida.\nNullam vel molestie justo. Curabitur vitae efficitur leo. In hac habitasse platea dictumst. Sed pulvinar mauris dui, eget varius purus congue ac. Nulla euismod, lorem vel elementum dapibus, nunc justo porta mi, sed tempus est est vel tellus. Nam et enim eleifend, laoreet sem sit amet, elementum sem. Morbi ut leo congue, maximus velit ut, finibus arcu. In et libero cursus, rutrum risus non, molestie leo. Nullam congue quam et volutpat malesuada. Sed risus tortor, pulvinar et dictum nec, sodales non mi. Phasellus lacinia commodo laoreet. Nam mollis, erat in feugiat consectetur, purus eros egestas tellus, in auctor urna odio at nibh. Mauris imperdiet nisi ac magna convallis, at rhoncus ligula cursus.\nCras aliquam rhoncus ipsum, in hendrerit nunc mattis vitae. Duis vitae efficitur metus, ac tempus leo. Cras nec fringilla lacus. Quisque sit amet risus at ipsum pharetra commodo. Sed aliquam mauris at consequat eleifend. Praesent porta, augue sed viverra bibendum, neque ante euismod ante, in vehicula justo lorem ac eros. Suspendisse augue libero, venenatis eget tincidunt ut, malesuada at lorem. Donec vitae bibendum arcu. Aenean maximus nulla non pretium iaculis. Quisque imperdiet, nulla in pulvinar aliquet, velit quam ultrices quam, sit amet fringilla leo sem vel nunc. Mauris in lacinia lacus.\nSuspendisse a tincidunt lacus. Curabitur at urna sagittis, dictum ante sit amet, euismod magna. Sed rutrum massa id tortor commodo, vitae elementum turpis tempus. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aenean purus turpis, venenatis a ullamcorper nec, tincidunt et massa. Integer posuere quam rutrum arcu vehicula imperdiet. Mauris ullamcorper quam vitae purus congue, quis euismod magna eleifend. Vestibulum semper vel augue eget tincidunt. Fusce eget justo sodales, dapibus odio eu, ultrices lorem. Duis condimentum lorem id eros commodo, in facilisis mauris scelerisque. Morbi sed auctor leo. Nullam volutpat a lacus quis pharetra. Nulla congue rutrum magna a ornare.\nAliquam in turpis accumsan, malesuada nibh ut, hendrerit justo. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Quisque sed erat nec justo posuere suscipit. Donec ut efficitur arcu, in malesuada neque. Nunc dignissim nisl massa, id vulputate nunc pretium nec. Quisque eget urna in risus suscipit ultricies. Pellentesque odio odio, tincidunt in eleifend sed, posuere a diam. Nam gravida nisl convallis semper elementum. Morbi vitae felis faucibus, vulputate orci placerat, aliquet nisi. Aliquam erat volutpat. Maecenas sagittis pulvinar purus, sed porta quam laoreet at.\n","date":1461715200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1461715200,"objectID":"e8f8d235e8e7f2efd912bfe865363fc3","permalink":"https://felixfeliz.github.io/project/example/","publishdate":"2016-04-27T00:00:00Z","relpermalink":"/project/example/","section":"project","summary":"An example of using the in-built project page.","tags":["Deep Learning"],"title":"Example Project","type":"project"},{"authors":null,"categories":null,"content":"","date":1461715200,"expirydate":-62135596800,"kind":"page","lang":"en","lastmod":1461715200,"objectID":"d1311ddf745551c9e117aa4bb7e28516","permalink":"https://felixfeliz.github.io/project/external-project/","publishdate":"2016-04-27T00:00:00Z","relpermalink":"/project/external-project/","section":"project","summary":"An example of linking directly to an external project website using `external_link`.","tags":["Demo"],"title":"External Project","type":"project"}]