Numerical Analysis of Partial Differential Equations
Computational Biomechanics of Skeletal Muscle
Finite Element Methods in Continuum Mechanics
Three-dimensional Musculoskeletal Simulation: Flexodeal

1. J.A. Almonacid and N. Nigam. Characterization of singular flows of zeroth-order pseudo-differential operators via elliptic eigenfunctions: a numerical study. Journal of Computational and Applied Mathematics 438 (2024) 115510. [arXiv:2210.13622] [GitHub Repo]
2. J.A. Almonacid, S.A. Dominguez-Rivera, R.N. Konno, N. Nigam, S.A. Ross, C. Tam, and J.M. Wakeling. A three-dimensional model of skeletal muscle tissues. SIAM Journal on Applied Mathematics 84 (2024), no. 3, S538-S566. [arXiv:2207.02421]
3. J.A. Almonacid, H. Díaz, G.N. Gatica and A. Márquez. A fully-mixed finite element method for the coupling of the Stokes and Darcy-Forchheimer problems. IMA J. Numer. Anal. 40 (2020), no. 2, 1454-1502.
4. J.A. Almonacid, G.N. Gatica, R. Oyarzúa and R. Ruiz-Baier. A new mixed finite element method for the n-dimensional Boussinesq problem with temperature-dependent viscosity. Netw. Heterog. Media (2020). https://doi.org/10.3934/nhm.2020010
5. J.A. Almonacid and G.N. Gatica. A fully-mixed finite element method for the n-dimensional Boussinesq problem with temperature-dependent parameters. Comput. Meth. Appl. Math. 20 (2020), no. 2, 187-213.
6. J.A. Almonacid, G.N. Gatica and R. Ruiz-Baier. Ultra-weak symmetry of stress for augmented mixed finite element formulations in continuum mechanics. Calcolo 57 (2020), Art. 2. https://doi.org/10.1007/s10092-019-0351-2.
7. J.A. Almonacid, G.N. Gatica and R. Oyarzúa. A posteriori error analysis of a mixed-primal finite element method for the Boussinesq problem with temperature-dependent viscosity. J. Sci. Comput. 78 (2019), no. 2, 887-917. Full-text view-only version: https://rdcu.be/4YAs.
8. J.A. Almonacid, G.N. Gatica and R. Oyarzúa. A mixed-primal finite element method for the Boussinesq problem with temperature-dependent viscosity. Calcolo 55 (2018), no. 3, Art. 36, 42 pp. Full-text view-only version: https://rdcu.be/32pk.

Internal Wave Attractors and Spectra of Zeroth-order Pseudo-Differential Operators. Supervisors: Nilima Nigam and Weiran Sun. In partial fullfillment of the requirements for the degree of Master of Science in Applied and Computational Mathematics, Department of Mathematics, Simon Fraser University (2020). [Thesis PDF][Defence Slides][GitHub]

Numerical Analysis of a Mixed Finite Element Method for the Boussinesq Problem with Temperature-Dependent Viscosity. Supervisors: Gabriel N. Gatica and Ricardo E. Oyarzúa. In partial fullfillment of the requirements for the professional title of "Mathematical Civil Engineer", Faculty of Physical and Mathematical Sciences, Universidad de Concepción (2017). [PDF]

1. Flexodeal: a new 3D finite element tool for studying musculoskeletal dynamics, at the 19th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering CMBBE 2024, Vancouver, BC. Joint work with the Neuromuscular Mechanics Laboratory.
2. Time stepping for nonlinear biological tissues: is first order enough?, at the World Congress on Computational Mechanics WCCM-PANACM 2024, Vancouver, BC. Joint work with Nilima Nigam and James Wakeling.
3. Nonlinear three-dimensional elastodynamics of skeletal muscle tissue, at the Cascade RAIN Meeting 2024, Portland, OR, United States. Joint work with Nilima Nigam and James Wakeling.
4. Characterization of singular flows of zeroth-order pseudo-differential operators via elliptic eigenfunctions, at the Seventh Workshop on Numerical Analysis of Partial Differential Equations WONAPDE 2024, Concepcion, Chile. Joint work with Nilima Nigam.
5. Modelling skeletal muscle tissue: three-dimensional dynamical models, at the Fourth Biennial Meeting of SIAM Pacific Northwest Section, Bellingham, WA, United States, 2023. Joint work with the Neuromuscular Mechanics Laboratory at SFU.
6. Modelling skeletal muscle tissue: inertial and stability considerations in one-dimensional models, at the Fourth Biennial Meeting of SIAM Pacific Northwest Section, Bellingham, WA, United States, 2023. Joint work with Ing-Jeng Chen, MD, Department of Biology Physiology and Kinesiology, SFU.
7. Finite-element discretization of a 3D hyperelastic model of skeletal muscle, at 2022 CMS Winter Meeting, Toronto, Canada. Co-authors: Neuromuscular Mechanics Laboratory (SFU).
8. Turbulence in the air: from data points to a heat map (an IPSW problem), at Grad SOCIAL Seminar Series, Department of Mathematics, Simon Fraser University, 2022.
9. Singular solutions and the spectrum of a zeroth-order pseudo-differential operator, at Cascade RAIN Meeting 2020. Virtual Conference. Co-authors: Nilima Nigam (SFU) and Maciej Zworski (UC Berkeley).[PDF]
10. Attractors and the spectrum of a zeroth-order pseudo-differential operator, at Miniconference on Sharp Eigenvalue Estimates for Partial Differential Operators (in lieu of the AMS Spring Sectional Meeting 2020, West Lafayette, IN, United States). Virtual Conference. Co-authors: Nilima Nigam (SFU) and Maciej Zworski (UC Berkeley).[PDF]
11. A posteriori error analysis of a mixed finite element method for nonisothermal flow, at CAIMS Annual Meeting 2019, Whistler, BC, Canada. Co-authors: Gabriel N. Gatica (UdeC) and Ricardo Oyarzua (UBB).
12. Mixed finite element methods for natural convection problems with nonconstant physical properties, at Young Researchers in Mathematics YRM2018, Southampton, United Kingdom. Co-authors: Gabriel N. Gatica (UdeC), Ricardo E. Oyarzúa (UBB) and Ricardo Ruiz Baier (Oxford).
13. A priori error analysis of a mixed-primal formulation for the Boussinesq problem with temperature-dependent viscosity, at XXVI Congreso de Matemática Capricornio COMCA-2017, Arica, Chile. Co-authors: Gabriel N. Gatica (UdeC), Ricardo E. Oyarzúa (UBB).
14. Research visits experience at SFU: Towards a valid approximation for the Neutron Transport Equation using Regularized Classical Half-Space Equations over the 2D unit disk, at Seminario de Análisis Numérico y Modelación Matemática (GIMNAP-UBB & CI²MA), Concepción, Chile. Co-authors: Weiran Sun (SFU).

1. Advances in Finite Elements & Applications to Fluid and Solid Mechanics, at 2022 CMS Winter Meeting. Joint organization with Nilima Nigam (SFU).

1. Numerical Methods for Spectral Problems NMSP2019, Research Institute for the Mathematical Sciences, Kyoto University, Kyoto, Japan.
2. Ninth Meeting on Numerical Analysis of Partial Differential Equations "Santiago Numérico III", 2017, Pontificia Universidad Catolica de Chile, Santiago, Chile.
3. Fifth Chilean Workshop on Numerical Analysis of Partial Differential Equations WONAPDE 2016, Universidad de Concepcion, Concepción, Chile.

1. Nonlinear elastodynamics simulations of skeletal muscle tissue, at SFU-UBC Applied Mathematics Day 2024, Simon Fraser University, Vancouver, BC.
2. Dynamic effects in nonlinear biological tissues and the Rothe's vs. method of lines dilemma, at Frontiers in Applied & Computational Mathematics (FACM) 2023, New Jersey Institute of Technology, Newark, NJ, United States.
3. Importance of mass in muscle models, at SFU BPK Research Day 2023, Burnaby, BC, Canada. Co-authors: Tania B. Gleeson & James M. Wakeling (Department of Biology, Physiology, and Kinesiology (BPK), SFU).
4. A parallel finite element solver for hyperelastic deformations, at Third Biennial Meeting of SIAM Pacific Northwest Section 2022, Vancouver, WA, United States.
5. High-order discretizations of a linear forced wave equation (Best Poster Award), at Second Biennial Meeting of SIAM Pacific Northwest Section 2019, Seattle, WA, United States. Co-authors: Nilima Nigam. [PDF]

1. Manufacture of contact lenses, presented by Johnson and Johnson Vision Care (Ireland) at the European Study Group with Industry (ESGI) 173, 2023, University of Limerick, Ireland.
2. Bubbles in flow streams and porous media, presented by W.L. Gore & Associates, Inc at the Mathematical Problems in Industry (MPI) 2023, New Jersey Institute of Technology, United States.
3. Modeling and evaluating risk for fire from rare weather events, presented by Manuchehr Aminian, Cal Poly Pomona, at the Graduate Student Mathematical Modelling Camp (GSMMC) 2023, University of Delaware, United States.
4. Turbulence in the air: creating a heat map and building a seasonal diagram, presented by the International Air Transport Association (IATA) at the 12th Montreal Industrial Problem Solving Workshop, 2022, Universite de Montreal, Canada. [Initial Presentation] [Final Presentation]